Game theory Books

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Book SynopsisAndreu Mas-Colell revolutionized our understanding of competitive markets, price formation, and the behavior of market participants. This volume presents the papers that solidified his standing as one of the preeminent economic theorists of our time. It also is invaluable for anyone wishing to study the craft of a master of economic modeling.

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Book SynopsisGull chicks beg for food from their parents. Peacocks spread their tails to attract potential mates. Meerkats alert family members of the approach of predators. But are these sometimes dishonest? This book probes such question by reviewing the empirical data and game theory models available, and by asking how well theory matches data.Trade Review"William Searcy and Stephen Nowicki provide a fascinating perspective on the honesty of signals in animal communication systems... [A] comprehensive yet concise review of what we currently know concerning signal reliability in animals, enriched with many in-depth examples."--Katherine E. LeVan and Noah Wilson-Rich, Science "The book is well written and informative... Searcy and Nowicki are well-known experts in the field of animal communication and sexual selection, and they provide a thorough and careful overview of this important, but often under-discussed, topic."--R. Andrew Hayes, Austral Ecology "The book is a fascinating evaluation of the present state of reliability and deception in animal signaling systems. It would make a perfect, albeit somewhat controversial, focus for an honors biology or graduate seminar course on animal communication."--H.Jane Brockmann, BioScienceTable of ContentsFigures, Boxes, and Table ix Acknowledgments xiii Introduction 1 Chapter 1: Definitions 2 Some History 6 Categories of Signal Costs 13 Alternative Explanations for Reliability 16 Deception Redux 17 Evolutionary Interests of Signalers and Receivers 20 Chapter 2: Signaling When Interests Overlap 24 Signaling Between Relatives: Theory 24 Begging 36 Alarms 53 Food Calls 68 Individually Directed Skepticism 73 Conclusions 77 Chapter 3: Signaling When Interests Diverge 78 Mating Signals: Theory 78 Carotenoid Pigmentation 86 Songs in Oscine Birds 97 Tail Length in Birds 123 Conclusions 131 Chapter 4: Signaling When Interests Oppose 134 Signaling in Aggressive Contexts: Theory 134 Postural Displays of Aggression in Birds 141 Badges of Status 147 Weapon Displays in Crustaceans 160 Dominant Frequency in Calls of Frogs and Toads 169 Conclusions 178 Chapter 5: Honesty and Deception in Communication Networks 181 Third-Party Receivers 182 "Eavesdropping" versus "Interception" 183 Eavesdropping in Signaling Interactions 185 Third-Party Receivers and Reliability 203 Conclusions 206 Chapter 6: Conclusions 207 Reliability 208 Alternatives to the Handicap Mechanism 214 Deceit 218 The Balance of Reliability and Deceit 223 References 225 Author Index 257 Subject Index 263

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Book SynopsisQuantal Response Equilibrium presents a stochastic theory of games that unites probabilistic choice models developed in psychology and statistics with the Nash equilibrium approach of classical game theory. Nash equilibrium assumes precise and perfect decision making in games, but human behavior is inherently stochastic and people realize that theTrade Review"This book brings together two decades of scholarship on an important model of boundedly rational behavior in strategic decision-making settings. Including numerous important applications in economics, political science, and pure game theory, this unified treatment will be valuable to a wide range of scholars."—Timothy Cason, Purdue University"Quantal response equilibrium is a standard tool for game theorists and has numerous connections to other tools and applications. This book collects and extends existing material on QRE and is a significant contribution to pure, and especially applied, game theory. No other books explicate QRE systematically beyond the introductory level and these authors are the right team for pulling the core material together."—Daniel Friedman, University of California, Santa Cruz"Well-written and easy to follow, this book covers the topic of quantal response equilibrium. The notion of stochastic equilibrium has changed the way game theorists think about long-run and short-run equilibrium. Written by three leading experts, this book is of great importance to researchers in economic theory and political science, and to graduate students."—David K. Levine, European University InstituteTable of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. ix*1. Introduction and Background, pg. 1*2. Quantal Response Equilibrium in Normal-Form Games, pg. 10*3. Quantal Response Equilibrium in Extensive-Form Games, pg. 63*4. Heterogeneity, pg. 88*5. Dynamics and Learning, pg. 112*6. QRE as a Structural Model for Estimation, pg. 141*7. Applications to Game Theory, pg. 161*8. Applications to Political Science, pg. 206*9. Applications to Economics, pg. 248*10. Epilogue: Some Thoughts about Future Research, pg. 281*References, pg. 291*Index, pg. 301

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Book SynopsisPublished in 1944, "Theory of Games and Economic Behavior" featured a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. This title includes the original text, an introduction by Harold Kuhn, and reviews and articles on the book that appeared at the time of its original publication.Trade ReviewPraise for Princeton's previous edition: "A rich and multifaceted work... [S]ixty years later, the Theory of Games may indeed be viewed as one of the landmarks of twentieth-century social science."--Robert J. Leonard, History of Political Economics Praise for Princeton's previous edition: "Opinions still vary on the success of the project to put economics on a sound mathematical footing, but game theory was eventually hugely influential, especially on mathematics and the study of automata. Every self-respecting library must have one."--Mike Holderness, New Scientist "While the jury is still out on the success or failure of game theory as an attempted palace coup within the economics community, few would deny that interest in the subject--as measured in numbers of journal page--is at or near an all-time high. For that reason alone, this handsome new edition of von Neumann and Morgenstern's still controversial classic should be welcomed by the entire research community."--James Case, SIAM News "The main achievement of the book lies, more than in its concrete results, in its having introduced into economics the tools of modern logic and in using them with an astounding power of generalization."--The Journal of Political Economy "One cannot but admire the audacity of vision, the perseverance in details, and the depth of thought displayed in almost every page of the book... The appearance of a book of [this] calibre ... is indeed a rare event."--The American Economic Review "Posterity may regard this book as one of the major scientific achievements of the first half of the twentieth century. This will undoubtedly be the case if the authors have succeeded in establishing a new exact science--the science of economics. The foundation which they have laid is extremely promising."--The Bulletin of the American Mathematical SocietyTable of ContentsPREFACE v TECHNICAL NOTE v ACKNOWLEDGMENT x CHAPTER I: FORMULATION OF THE ECONOMIC PROBLEM 1.THE MATHEMATICAL METHOD IN ECONOMICS 1 1.1. Introductory remarks 1 1.2. Difficulties of the application of the mathematical method 2 1.3. Necessary limitations of the objectives 6 1.4. Concluding remarks 7 2.QUALITATIVE DISCUSSION OF THE PROBLEM OF RATIONAL BEHAVIOR 8 2.1. The problem of rational behavior 8 2.2. "Robinson Crusoe" economy and social exchange economy 9 2.3. The number of variables and the number of participants 12 2.4. The case of many participants: Free competition 13 2.5. The "Lausanne" theory 15 3.THE NOTION OF UTILITY 15 3.1. Preferences and utilities 15 3.2. Principles of measurement: Preliminaries 16 3.3. Probability and numerical utilities 17 3.4. Principles of measurement: Detailed discussion 20 3.5. Conceptual structure of the axiomatic treatment of numerical utilities 24 3.6. The axioms and their interpretation 26 3.7. General remarks concerning the axioms 28 3.8. The role of the concept of marginal utility 29 4.STRUCTURE OF THE THEORY: SOLUTIONS AND STANDARDS OF BEHAVIOR 31 4.1. The simplest concept of a solution for one participant 31 4.2. Extension to all participants 33 4.3. The solution as a set of imputations 34 4.4. The intransitive notion of "superiority" or "domination" 37 4.5. The precise definition of a solution 39 4.6. Interpretation of our definition in terms of "standards of behavior" 40 4.7. Games and social organizations 43 4.8. Concluding remarks 43 CHAPTER II: GENERAL FORMAL DESCRIPTION OF GAMES OF STRATEGY 5.Introduction 46 5.1. Shift of emphasis from economics to games 46 5.2. General principles of classification and of procedure 46 6.THE SIMPLIFIED CONCEPT OF A GAME 48 6.1. Explanation of the termini technici 48 6.2. The elements of the game 49 6.3. Information and preliminary 51 6.4. Preliminarity, transitivity, and signaling 51 7.THE COMPLETE CONCEPT OF A GAME 55 7.1. Variability of the characteristics of each move 55 7.2. The general description 57 8.SETS AND PARTITIONS 60 8.1. Desirability of a set-theoretical description of a game 60 8.2. Sets, their properties, and their graphical representation 61 8.3. Partitions, their properties, and their graphical representation 63 8.4. Logistic interpretation of sets and partitions 66 *9. THE SET-THEORETICAL DESCRIPTION OF A CAME 67 *9.1. The partitions which describe a game 67 *9.2. Discussion of these partitions and their properties 71 *10. AXIOMATIC FORMULATION 73 *10.1. The axioms and their interpretations 73 *10.2. Logistic discussion of the axioms 76 *10.3. General remarks concerning the axioms 76 *10.4. Graphical representation 77 11.STRATEGIES AND THE FINAL SIMPLIFICATION OF THE DESCRIPTION OF THE GAME 79 11.1. The concept of a strategy and its formalization 79 11.2. The final simplification of the description of a game 81 11.3. The role of strategies in the simplified form of a game 84 11.4. The meaning of the zero-sum restriction 84 CHAPTER III: ZERO-SUM TWO-PERSON GAMES: THEORY 12.PRELIMINARY SURVEY 85 12.1. General viewpoints 85 12.2. The one-person game 85 12.3. Chance afid probability 87 12.4. The next objective 87 13.FUNCTIONAL CALCULUS 88 13.1. Basic definitions 88 13.2. The operations Max and Min 89 13.3. Commutativity questions 91 13.4. The mixed case. Saddle points 93 13.5. Proofs of the main facts 95 14.STRICTLY DETERMINED GAMES 98 141. Formulation of the problem 98 14.2. The minorant and the majorant games 100 14.3. Discussion of the auxiliary games 101 14.4. Conclusions 105 14.5. Analysis of strict determinateness 106 14.6. The interchange of players. Symmetry 109 14.7. Non strictly determined games 110 14.8. Program of a detailed analysis of strict determinateness 111 *15. GAMES WITH PERFECT INFORMATION *15.1. Statement of purpose. Induction 112 *15.2. The exact condition (First step) 114 *15.3. The exact condition (Entire induction) 116 *15.4. Exact discussion of the inductive step 117 *15.5. Exact discussion of the inductive step (Continuation) 120 *15.6. The result in the case of perfect information 123 *15.7. Application to Chess 124 *15.8. The alternative, verbal discussion 126 16.LINEARITY AND CONVEXITY 128 16.1. Geometrical background 128 16.2. Vector operations 129 16.3. The theorem of the supporting hyperplanes 134 16.4. The theorem of the alternative for matrices 138 17.MIXED STRATEGIES. THE SOLUTION FOR ALL GAMES 143 17.1. Discussion of two elementary examples 143 17.2. Generalization of this viewpoint 145 17.3. Justification of the procedure as applied to an individual play 146 17.4. The minorant and the majorant games. (For mixed strategies) 149 17.5. General strict determinateness 150 17.6. Proof of the main theorem 153 17.7. Comparison of the treatment by pure and by mixed strategies 155 17.8. Analysis of general strict determinateness 158 17.9. Further characteristics of good strategies 160 17.10. Mistakes and their consequences. Permanent optimality 162 17.11. The interchange of players. Symmetry 165 CHAPTER IV: ZERO-SUM TWO-PERSON GAMES: EXAMPLES 18.SOME ELEMENTARY GAMES 169 18.1. The simplest games 169 18.2. Detailed quantitative discussion of these games 170 18.3. Qualitative characterizations 173 18.4. Discussion of some specific games. (Generalized forms of Matching Pennies) 175 18.5. Discussion of some slightly more complicated games 178 18.6. Chance and imperfect information 182 18.7. Interpretation of this result 185 *19. POKER AND BLUFFING 186 *19.1. Description of Poker 186 *19.2. Bluffing 188 *19.3. Description of Poker (Continued) 189 *19.4. Exact formulation of the rules 190 *19.5. Description of the strategy 191 *19.6. Statement of the problem 195 *19.7. Passage from the discrete to the continuous problem 196 *19.8. Mathematical determination of the solution 199 *19.9. Detailed analysis of the solution 202 *19.10. Interpretation of the solution 204 *19.11. More general forms of Poker 207 *19.12. Discrete hands 208 *19.13. m possible bids 209 *19.14. Alternate bidding 211 *19.15. Mathematical description of all solutions 216 *19.16. Interpretation of the solutions. Conclusions 218 CHAPTER V: ZERO-SUM THREE-PERSON GAMES 20.PRELIMINARY SURVEY 220 20.1. General viewpoints 220 20.2. Coalitions 221 21.THE SIMPLE MAJORITY GAME OF THREE PERSONS 222 21.1. Definition of the game 222 21.2. Analysis of the game: Necessity of "understandings" 223 21.3. Analysis of the game: Coalitions. The role of symmetry 224 22.FURTHER EXAMPLES 225 22.1. Unsymmetric distributions. Necessity of compensations 225 22.2. Coalitions of different strength. Discussion 227 22.3. An inequality. Formulae 229 23.THE GENERAL CASE 231 23.1. Detailed discussion. Inessential and essential games 231 23.2. Complete formulae 232 24.DISCUSSION OF AN OBJECTION 233 24.1. The case of perfect information and its significance 233 24.2. Detailed discussion. Necessity of compensations between three or more players 235 CHAPTER VI: FORMULATION OF THE GENERAL THEORY: ZERO-SUM n-PERSON GAMES 25.THE CHARACTERISTIC FUNCTION 238 25.1. Motivation and definition 238 25.2. Discussion of the concept 240 25.3. Fundamental properties 241 25.4. Immediate mathematical consequences 242 26.CONSTRUCTION OF A GAME WITH A GIVEN CHARACTERISTIC FUNCTION 243 26.1. The construction 243 26.2. Summary 245 27.STRATEGIC EQUIVALENCE. INESSENTIAL AND ESSENTIAL GAMES 245 27.1. Strategic equivalence. The reduced form 245 27.2. Inequalities. The quantity [gamma] 248 27.3. Inessentiality and essentiality 249 27.4. Various criteria. Non additive utilities 250 27.5. The inequalities in the essential case 252 27.6. Vector operations on characteristic functions 253 28.GROUPS, SYMMETRY AND FAIRNESS 255 28.1. Permutations, their groups and their effect on a game 255 28.2. Symmetry and fairness 258 29.RECONSIDERATION OF THE ZERO-SUM THREE-PERSON GAME 260 29.1. Qualitative discussion 260 29.2. Quantitative discussion 262 30.THE EXACT FORM OF THE GENERAL DEFINITIONS 263 30.1. The definitions 263 30.2. Discussion and recapitulation 265 *30.3. The concept of saturation 266 30.4. Three immediate objectives 271 31.FIRST CONSEQUENCES 272 31.1. Convexity, flatness, and some criteria for domination 272 31.2. The system of all imputations. One element solutions 277 31.3. The isomorphism which corresponds to strategic equivalence 281 32.DETERMINATION OF ALL SOLUTIONS OF THE ESSENTIAL ZERO-SUM THREE-PERSON GAME 282 32.1. Formulation of the mathematical problem. The graphical method 282 32.2. Determination of all solutions 285 33.CONCLUSIONS 288 33.1. The multiplicity of solutions. Discrimination and its meaning 288 33.2. Statics and dynamics 290 CHAPTER VII: ZERO-SUM FOUR-PERSON GAMES 34.PRELIMINARY SURVEY 291 34.1. General viewpoints 291 34.2. Formalism of the essential zero sum four person games 291 34.3. Permutations of the players 294 35.DISCUSSION OF SOME SPECIAL POINTS IN THE CUBE Q 295 35.1. The corner I. (and V., VI., VII.) 295 35.2. The corner VIII. (and II., III., IV.,). The three person game and a "Dummy" 299 35.3. Some remarks concerning the interior of Q 302 36.DISCUSSION OF THE MAIN DIAGONALS 304 36.1. The part adjacent to the corner VIII.: Heuristic discussion 304 36.2. The part adjacent to the corner VIII.: Exact discussion 307 *36.3. Other parts of the main diagonals 312 37.THE CENTER AND ITS ENVIRONS 313 37.1. First orientation about the conditions around the center 313 37.2. The two alternatives and the role of symmetry 315 37.3. The first alternative at the center 316 37.4. The second alternative at the center 317 37.5. Comparison of the two central solutions 318 37.6. Unsymmetrical central solutions 319 *38. A FAMILY OF SOLUTIONS FOR A NEIGHBORHOOD OF THE CENTER 321 *38.1. Transformation of the solution belonging to the first alternative at the center 321 *38.2. Exact discussion 322 *38.3. Interpretation of the solutions 327 CHAPTER VIII: SOME REMARKS CONCERNING n [equal to or greater than] 5 PARTICIPANTS 39.THE NUMBER OF PARAMETERS IN VARIOUS CLASSES OF GAMES 330 39.1. The situation for n = 3, 4 330 39.2. The situation for all n [equal to or greater than] 3 330 40.THE SYMMETRIC FIVE PERSON GAME 332 40.1. Formalism of the symmetric five person game 332 40.2. The two extreme cases 332 40.3. Connection between the symmetric five person game and the 1, 2, 3 symmetric four person game 334 CHAPTER IX: COMPOSITION AND DECOMPOSITION OF GAMES 41.COMPOSITION AND DECOMPOSITION 339 41.1. Search for n-person games for which all solutions can be determined 339 41.2. The first type. Composition and decomposition 340 41.3. Exact definitions 341 41.4. Analysis of decomposability 343 41.5. Desirability of a modification 345 42.MODIFICATION OF THE THEORY 345 42.1. No complete abandonment of the zero sum restriction 345 42.2. Strategic equivalence. Constant sum games 346 42.3. The characteristic function in the new theory 348 42.4. Imputations, domination, solutions in the new theory 350 42.5. Essentiality, inessentiality and decomposability in the new theory 351 43.THE DECOMPOSITION PARTITION 353 43.1. Splitting sets. Constituents 353 43.2. Properties of the system of all splitting sets 353 43.3. Characterization of the system of all splitting sets. The decomposition partition 354 43.4. Properties of the decomposition partition 357 44.DECOMPOSABLE GAMES. FURTHER EXTENSION OF THE THEORY 358 44.1. Solutions of a (decomposable) game and solutions of its constituents 358 44.2. Composition and decomposition of imputations and of sets of imputations 359 44.3. Composition and decomposition of solutions. The main possibilities and surmises 361 44.4. Extension of the theory. Outside sources 363 44.5. The excess 364 44.6. Limitations of the excess. The non-isolated character of a game in the new setup 366 44.7. Discussion of the new setup. E(e0), F(e0) 367 45.LIMITATIONS OF THE EXCESS. STRUCTURE OF THE EXTENDED THEORY 378 45.1. The lower limit of the excess 368 45.2. The upper limit of the excess. Detached and fully detached imputations 369 45.3. Discussion of the two limits, |[Gamma]|1, |[Gamma]|2. Their ratio 372 45.4. Detached imputations and various solutions. The theorem connecting E(e0), F(e0) 375 45.5. Proof of the theorem 376 45.6. Summary and conclusions 380 46.DETERMINATION OF ALL SOLUTIONS OF A DECOMPOSABLE GAME 381 46.1. Elementary properties of decompositions 381 46.2. Decomposition and its relation to the solutions: First results concerning F(e0) 384 46.3. Continuation 386 46.4. Continuation 388 46.5. The complete result in F(e0) 390 46.6. The complete result in E(e0) 393 46.7. Graphical representation of a part of the result 394 46.8. Interpretation: The normal zone. Heredity of various properties 396 46.9. Dummies 397 46.10. Imbedding of a game 398 46.11. Significance of the normal zone 401 46.12. First occurrence of the phenomenon of transfer: n = 6 402 47.THE ESSENTIAL THREE-PERSON GAME IN THE NEW THEORY 403 47.1. Need for this discussion 403 47.2. Preparatory considerations 403 47.3. The six cases of the discussion. Cases (I)-(III) 406 47.4. Case (IV): First part 407 47.5. Case (IV): Second part 409 47.6. Case (V) 413 47.7. Case (VI) 415 47.8. Interpretation of the result: The curves (one dimensional parts) in the solution 416 47.9. Continuation: The areas (two dimensional parts) in the solution 418 CHAPTER X: SIMPLE GAMES 48.WINNING AND LOSING COALITIONS AND GAMES WHERE THEY OCCUR 420 48.1. The second type of 41.1. Decision by coalitions 420 48.2. Winning and Losing Coalitions 421 49.CHARACTERIZATION OF THE SIMPLE GAMES 423 49.1. General concepts of winning and losing coalitions 423 49.2. The special role of one element sets 425 49.3. Characterization of the systems W, L of actual games 426 49.4. Exact definition of simplicity 428 49.5. Some elementary properties of simplicity 428 49.6. Simple games and their W, L. The Minimal winning coalitions: Wm 429 49.7. The solutions of simple games 430 50.THE MAJORITY GAMES AND THE MAIN SOLUTION 431 50.1. Examples of simple games: The majority games 481 50.2. Homogeneity 433 50.3. A more direct use of the concept of imputation in forming solutions 435 50.4. Discussion of this direct approach 436 50.5. Connections with the general theory. Exact formulation 438 50.6. Reformulation of the result 440 50.7. Interpretation of the result 442 50.8. Connection with the Homogeneous Majority game 443 51.METHODS FOR THE ENUMERATION OF ALL SIMPLE GAMES 445 51.1. Preliminary Remarks 445 51.2. The saturation method: Enumeration by means of W 446 51.3. Reasons for passing from W to Wm. Difficulties of using Wm 448 51.4. Changed Approach: Enumeration by means of Wm 450 51.5. Simplicity and decomposition 452 51.6. Inessentiality, Simplicity and Composition. Treatment of the excess 454 51.7. A criterium of decomposability in terms of Wm 455 52.THE SIMPLE GAMES FOR SMALL n 457 52.1. Program. n = 1, 2 play no role. Disposal of n = 3 457 52.2. Procedure for n [equal to or greater than] 4: The two element sets and their role in classify ing the Wm 458 52.3. Decomposability of cases C*, Cn-2, Cn-1 459 52.4. The simple games other than [1, ... , 1, n - 2]h, (with dummies): The Cases Ck, k = 0, 1, ... , n - 3 461 52.5. Disposal of n = 4, 5 462 53.THE NEW POSSIBILITIES OF SIMPLE GAMES FOR n [equal to or greater than] 6 463 53.1. The Regularities observed for n [equal to or greater than] 6 463 53.2. The six main counter examples (for n = 6, 7) 464 54.DETERMINATION OF ALL SOLUTIONS IN SUITABLE GAMES 470 54.1. Reasons to consider other solutions than the main solution in simple games 470 54.2. Enumeration of those games for which all solutions are known 471 54.3. Reasons to consider the simple game [1, ... , 1, n - 2]h, 472 *55. THE SIMPLE GAME [1, ... , 1, n - 2]h 473 *55.1. Preliminary Remarks 473 *55.2. Domination. The chief player. Cases (I) and (11) 473 *55.3. Disposal of Case (I) 475 *55.4. Case (II): Determination of V [above horizontal bar] 478 *55.5. Case (II): Determination of V [below horizontal bar] 481 *55.6. Case (II): [alpha] and S* 484 *55.7. Case (II') and (II"). Disposal of Case (II') 485 *55.8. Case (II"): [alpha] and V'. Domination 488 *55.9. Case (II"): Determination of V' *55.10. Disposal of Case (II") 488 *55.11. Reformulation of the complete result 497 *55.12. Interpretation of the result 499 CHAPTER XI: GENERAL NON-ZERO-SUM GAMES 56.EXTENSION OF THE THEORY 504 56.1. Formulation of the problem 504 56.2. The fictitious player. The zero sum extension [Gamma] 505 56.3. Questions concerning the character of [Gamma below horizontal bar] 506 56.4. Limitations of the use of [Gamma above horizontal bar] 508 56.5. The two possible procedures 510 56.6. The discriminatory solutions 511 56.7. Alternative possibilities 512 56.8. The new setup 514 56.9. Reconsideration of the case when [Gamma] is a zero sum game 516 56.10. Analysis of the concept of domination 520 56.11. Rigorous discussion 523 56.12. The new definition of a solution 526 57.THE CHARACTERISTIC FUNCTION AND RELATED TOPICS 527 57.1. The characteristic function: The extended and the restricted form 527 57.2. Fundamental properties 528 57.3. Determination of all characteristic functions 530 57.4. Removable sets of players 533 57.5. Strategic equivalence. Zero-sum and constant-sum games 535 58.INTERPRETATION OF THE CHARACTERISTIC FUNCTION 538 58.1. Analysis of the definition 538 58.2. The desire to make a gain vs. that to inflict a loss 539 58.3. Discussion 541 59.GENERAL CONSIDERATIONS 542 59.1. Discussion of the program 542 59.2. The reduced forms. The inequalities 543 59.3. Various topics 546 60.THE SOLUTIONS OF ALL GENERAL GAMES WITH n [equal to or less than] 3 548 60.1. The case n = 1 548 60.2. The case n = 2 549 60.3. The case n = 3 550 60.4. Comparison with the zero sum games 554 61.ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 1, 2 555 61.1. The case n = 1 555 61.2. The case n = 2. The two person market 555 61.3. Discussion of the two person market and its characteristic function 557 61.4. Justification of the standpoint of 58 559 61.5. Divisible goods. The "marginal pairs" 560 61.6. The price. Discussion 562 62.ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: SPECIAL CASE 564 62.1. The case n = 3, special case. The three person market 564 62.2. Preliminary discussion 566 62.3. The solutions: First subcase 566 62.4. The solutions: General form 569 62.5. Algebraical form of the result 570 62.6. Discussion 571 63.ECONOMIC INTERPRETATION OF THE RESULTS FOR n = 3: GENERAL CASE 573 63.1. Divisible goods 573 63.2. Analysis of the inequalities 575 63.3. Preliminary discussion 577 63.4. The solutions 577 63.5. Algebraical form of the result 580 63.6. Discussion 581 64.THE GENERAL MARKET 583 64.1. Formulation of the problem 583 64.2. Some special properties. Monopoly and monopsony 584 CHAPTER XII: EXTENSION OF THE CONCEPTS OF DOMINATION AND SOLUTION 65.THE EXTENSION. SPECIAL CASES 587 65.1. Formulation of the problem 587 65.2. General remarks 588 65.3. Orderings, transitivity, acyclicity 589 65.4. The solutions: For a symmetric relation. For a complete ordering 591 65.5. The solutions: For a partial ordering 592 65.6. Acyclicity and strict acyclicity 594 65.7. The solutions: For an acyclic relation 597 65.8. Uniqueness of solutions, acyclicity and strict acyclicity 600 65.9. Application to games: Discreteness and continuity 602 66.GENERALIZATION OF THE CONCEPT OF UTILITY 603 66.1. The generalization. The two phases of the theoretical treatment 603 66.2. Discussion of the first phase 604 66.3. Discussion of the second phase 606 66.4. Desirability of unifying the two phases 607 67.DISCUSSION OF AN EXAMPLE 608 67.1. Description of the example 608 67.2. The solution and its interpretation 611 67.3. Generalization: Different discrete utility scales 614 67.4. Conclusions concerning bargaining 616 APPENDIX: THE AXIOMATIC TREATMENT OF UTILITY 617 INDEX OF FIGURES 633 INDEX OF NAMES 634 INDEX OF SUBJECTS 635

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Book SynopsisFocusing on evolutionary game theory, this textbook shows students how to apply game theory to model human behavior in ways that reflect the special nature of sociality and individuality. It also includes solutions to the problems presented and information related to agent-based modeling.Trade Review"Gintis has wholeheartedly embraced the evolutionary approach to games... The author is an accomplished economist raised in the classical mold, and his background shows in many aspects of the book ... [He] has important things to say."--Karl Sigmund, Science "Game Theory Evolving is an exceptionally well-written and constructed introduction to the field. And with Gintis' outline of agent-based modeling and his tips for programming, many readers may be motivated to take up his invitation and experiment with a problem in evolutionary dynamics of their own."--Jennifer M. Wilson, Mathematical ReviewsTable of ContentsPreface xv Chapter 1: Probability Theory 1 1.1 Basic Set Theory and Mathematical Notation 1 1.2 Probability Spaces 2 1.3 De Morgan's Laws 3 1.4 Interocitors 3 1.5 The Direct Evaluation of Probabilities 3 1.6 Probability as Frequency 4 1.7 Craps 5 1.8 A Marksman Contest 5 1.9 Sampling 5 1.10 Aces Up 6 1.11 Permutations 6 1.12 Combinations and Sampling 7 1.13 Mechanical Defects 7 1.14 Mass Defection 7 1.15 House Rules 7 1.16 The Addition Rule for Probabilities 8 1.17 A Guessing Game 8 1.18 North Island, South Island 8 1.19 Conditional Probability 9 1.20 Bayes' Rule 9 1.21 Extrasensory Perception 10 1.22 Les Cinq Tiroirs 10 1.23 Drug Testing 10 1.24 Color Blindness 11 1.25 Urns 11 1.26 The Monty Hall Game 11 1.27 The Logic of Murder and Abuse 11 1.28 The Principle of Insufficient Reason 12 1.29 The Greens and the Blacks 12 1.30 The Brain and Kidney Problem 12 1.31 The Value of Eyewitness Testimony 13 1.32 When Weakness Is Strength 13 1.33 The Uniform Distribution 16 1.34 Laplace's Law of Succession 17 1.35 From Uniform to Exponential 17 Chapter 2: Bayesian Decision Theory 18 2.1 The Rational Actor Model 18 2.2 Time Consistency and Exponential Discounting 20 2.3 The Expected Utility Principle 22 2.4 Risk and the Shape of the Utility Function 26 2.5 The Scientific Status of the Rational Actor Model 30 Chapter 3: Game Theory: Basic Concepts 32 3.1 Big John and Little John 32 3.2 The Extensive Form 38 3.3 The Normal Form 41 3.4 Mixed Strategies 42 3.5 Nash Equilibrium 43 3.6 The Fundamental Theorem of Game Theory 44 3.7 Solving for Mixed-Strategy Nash Equilibria 44 3.8 Throwing Fingers 46 3.9 Battle of the Sexes 46 3.10 The Hawk-Dove Game 48 3.11 The Prisoner's Dilemma 50 Chapter 4: Eliminating Dominated Strategies 52 4.1 Dominated Strategies 52 4.2 Backward Induction 54 4.3 Exercises in Eliminating Dominated Strategies 55 4.4 Subgame Perfection 57 4.5 Stackelberg Leadership 59 4.6 The Second-Price Auction 59 4.7 The Mystery of Kidnapping 60 4.8 The Eviction Notice 62 4.9 Hagar's Battles 62 4.10 Military Strategy 63 4.11 The Dr. Strangelove Game 64 4.12 Strategic Voting 64 4.13 Nuisance Suits 65 4.14 An Armaments Game 67 4.15 Football Strategy 67 4.16 Poker with Bluffing 68 4.17 The Little Miss Muffet Game 69 4.18 Cooperation with Overlapping Generations 70 4.19 Dominance-Solvable Games 71 4.20 Agent-based Modeling 72 4.21 Why Play a Nash Equilibrium? 75 4.22 Modeling the Finitely-Repeated Prisoner's Dilemma 77 4.23 Review of Basic Concepts 79 Chapter 5: Pure-Strategy Nash Equilibria 80 5.1 Price Matching as Tacit Collusion 80 5.2 Competition on Main Street 81 5.3 Markets as Disciplining Devices: Allied Widgets 81 5.4 The Tobacco Market 87 5.5 The Klingons and the Snarks 87 5.6 Chess: The Trivial Pastime 88 5.7 No-Draw, High-Low Poker 89 5.8 An Agent-based Model of No-Draw, High-Low Poker 91 5.9 The Truth Game 92 5.10 The Rubinstein Bargaining Model 94 5.11 Bargaining with Heterogeneous Impatience 96 5.12 Bargaining with One Outside Option 97 5.13 Bargaining with Dual Outside Options 98 5.14 Huey, Dewey, and Louie Split a Dollar 102 5.15 Twin Sisters 104 5.16 The Samaritan's Dilemma 104 5.17 The Rotten Kid Theorem 106 5.18 The Shopper and the Fish Merchant 107 5.19 Pure Coordination Games 109 5.20 Pick Any Number 109 5.21 Pure Coordination Games: Experimental Evidence 110 5.22 Introductory Offers 111 5.23 Web Sites (for Spiders) 112 Chapter 6: Mixed-Strategy Nash Equilibria 116 6.1 The Algebra of Mixed Strategies 116 6.2 Lions and Antelope 117 6.3 A Patent Race 118 6.4 Tennis Strategy 119 6.5 Preservation of Ecology Game 119 6.6 Hard Love 120 6.7 Advertising Game 120 6.8 Robin Hood and Little John 122 6.9 The Motorist's Dilemma 122 6.10 Family Politics 123 6.11 Frankie and Johnny 123 6.12 A Card Game 124 6.13 Cheater-Inspector 126 6.14 The Vindication of the Hawk 126 6.15 Characterizing 2 x 2 Normal Form Games I 127 6.16 Big John and Little John Revisited 128 6.17 Dominance Revisited 128 6.18 Competition on Main Street Revisited 128 6.19 Twin Sisters Revisited 129 6.20 Twin Sisters: An Agent-Based Model 129 6.21 One-Card, Two-Round Poker with Bluffing 131 6.22 An Agent-Based Model of Poker with Bluffing 132 6.23 Trust in Networks 133 6.24 El Farol 134 6.25 Decorated Lizards 135 6.26 Sex Ratios as Nash Equilibria 137 6.27 A Mating Game 140 6.28 Coordination Failure 141 6.29 Colonel Blotto Game 141 6.30 Number Guessing Game 142 6.31 Target Selection 142 6.32 A Reconnaissance Game 142 6.33 Attack on Hidden Object 143 6.34 Two-Person, Zero-Sum Games 143 6.35 Mutual Monitoring in a Partnership 145 6.36 Mutual Monitoring in Teams 145 6.37 Altruism(?) in Bird Flocks 146 6.38 The Groucho Marx Game 147 6.39 Games of Perfect Information 151 6.40 Correlated Equilibria 151 6.41 Territoriality as a Correlated Equilibrium 153 6.42 Haggling at the Bazaar 154 6.43 Poker with Bluffing Revisited 156 6.44 Algorithms for Finding Nash Equilibria 157 6.45 Why Play Mixed Strategies? 160 6.46 Reviewing of Basic Concepts 161 Chapter 7: Principal-AgentModels 162 7.1 Gift Exchange 162 7.2 Contract Monitoring 163 7.3 Profit Signaling 164 7.4 Properties of the Employment Relationship 168 7.5 Peasant and Landlord 169 7.6 Bob's Car Insurance 173 7.7 A Generic Principal-Agent Model 174 Chapter 8: Signaling Games 179 8.1 Signaling as a Coevolutionary Process 179 8.2 A Generic Signaling Game 180 8.3 Sex and Piety: The Darwin-Fisher Model 182 8.4 Biological Signals as Handicaps 187 8.5 The ShepherdsWho Never Cry Wolf 189 8.6 My Brother's Keeper 190 8.7 Honest Signaling among Partial Altruists 193 8.8 Educational Signaling 195 8.9 Education as a Screening Device 197 8.10 Capital as a Signaling Device 199 Chapter 9: Repeated Games 201 9.1 Death and Discount Rates in Repeated Games 202 9.2 Big Fish and Little Fish 202 9.3 Alice and Bob Cooperate 204 9.4 The Strategy of an Oil Cartel 205 9.5 Reputational Equilibrium 205 9.6 Tacit Collusion 206 9.7 The One-Stage Deviation Principle 208 9.8 Tit for Tat 209 9.9 I'd Rather Switch Than Fight 210 9.10 The Folk Theorem 213 9.11 The Folk Theorem and the Nature of Signaling 216 9.12 The Folk Theorem Fails in Large Groups 217 9.13 Contingent Renewal Markets Do Not Clear 219 9.14 Short-Side Power in Contingent Renewal Markets 222 9.15 Money Confers Power in Contingent Renewal Markets 223 9.16 The Economy Is Controlled by the Wealthy 223 9.17 Contingent Renewal Labor Markets 224 Chapter 10: Evolutionarily Stable Strategies 229 10.1 Evolutionarily Stable Strategies: Definition 230 10.2 Properties of Evolutionarily Stable Strategies 232 10.3 Characterizing Evolutionarily Stable Strategies 233 10.4 A Symmetric Coordination Game 236 10.5 A Dynamic Battle of the Sexes 236 10.6 Symmetrical Throwing Fingers 237 10.7 Hawks, Doves, and Bourgeois 238 10.8 Trust in Networks II 238 10.9 Cooperative Fishing 238 10.10 Evolutionarily Stable Strategies Are Not Unbeatable 240 10.11 A Nash Equilibrium That Is Not an EES 240 10.12 Rock, Paper, and Scissors Has No ESS 241 10.13 Invasion of the Pure-Strategy Mutants 241 10.14 Multiple Evolutionarily Stable Strategies 242 10.15 Evolutionarily Stable Strategies in Finite Populations 242 10.16 Evolutionarily Stable Strategies in Asymmetric Games 244 Chapter 11: Dynamical Systems 247 11.1 Dynamical Systems: Definition 247 11.2 Population Growth 248 11.3 Population Growth with Limited Carrying Capacity 249 11.4 The Lotka-Volterra Predator-Prey Model 251 11.5 Dynamical Systems Theory 255 11.6 Existence and Uniqueness 256 11.7 The Linearization Theorem 257 11.8 Dynamical Systems in One Dimension 258 11.9 Dynamical Systems in Two Dimensions 260 11.10 Exercises in Two-Dimensional Linear Systems 264 11.11 Lotka-Volterra with Limited Carrying Capacity 266 11.12 Take No Prisoners 266 11.13 The Hartman-Grobman Theorem 267 11.14 Features of Two-Dimensional Dynamical Systems 268 Chapter 12: Evolutionary Dynamics 270 12.1 The Origins of Evolutionary Dynamics 271 12.2 Strategies as Replicators 272 12.3 A Dynamic Hawk-Dove Game 274 12.4 Sexual Reproduction and the Replicator Dynamic 276 12.5 Properties of the Replicator System 278 12.6 The Replicator Dynamic in Two Dimensions 279 12.7 Dominated Strategies and the Replicator Dynamic 280 12.8 Equilibrium and Stability with a Replicator Dynamic 282 12.9 Evolutionary Stability and Asymptotically Stability 284 12.10 Trust in Networks III 284 12.11 Characterizing 2 x 2 Normal Form Games II 285 12.12 Invasion of the Pure-Strategy Nash Mutants II 286 12.13 A Generalization of Rock, Paper, and Scissors 287 12.14 Uta stansburiana in Motion 287 12.15 The Dynamics of Rock, Paper, and Scissors 288 12.16 The Lotka-VolterraModel and Biodiversity 288 12.17 Asymmetric Evolutionary Games 290 12.18 Asymmetric Evolutionary Games II 295 12.19 The Evolution of Trust and Honesty 295 Chapter 13: Markov Economies and Stochastic Dynamical Systems 297 13.1 Markov Chains 297 13.2 The Ergodic Theorem for Markov Chains 305 13.3 The Infinite Random Walk 307 13.4 The Sisyphean Markov Chain 308 13.5 Andrei Andreyevich's Two-Urn Problem 309 13.6 Solving Linear Recursion Equations 310 13.7 Good Vibrations 311 13.8 Adaptive Learning 312 13.9 The Steady State of a Markov Chain 314 13.10 Adaptive Learning II 315 13.11 Adaptive Learning with Errors 316 13.12 Stochastic Stability 317 Chapter 14: Table of Symbols 319 Chapter 15: Answers 321 Sources for Problems 373 References 375

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Book SynopsisA wealth of research in recent decades has seen the economic approach to human behavior extended over many areas previously considered to belong to sociology, political science, law, and other fields. This book uses soccer to test economic theories and document novel human behavior.Trade Review"[E]njoyably accessible to nonspecialists, especially sports enthusiasts, who will learn a great deal about soccer, economics, and human behavior more generally."--Foreign Affairs "Beautiful Game Theory shows what it is like to think deeply about a sport and to test your ideas with data... [I]t is a book I recommend unconditionally to those economists with even a passing sport."--John Considine, Sportseconomics.orgTable of ContentsIntroduction 1 FIRST HALF 1.Pele Meets John von Neumann in the Penalty Area 9 2.Vernon Smith Meets Messi in the Laboratory 31 3.Lessons for Experimental Design 45 4.Mapping Minimax in the Brain (with Antonio Olivero, Sven Bestmann, Jose Florensa Vila, and Jose Apesteguia) 58 5.Psychological Pressure on the Field and Elsewhere 68 HALFTIME 6.Scoring at Halftime 89 SECOND HALF 7.Favoritism under Social Pressure 107 8.Making the Beautiful Game a Bit Less Beautiful (with Luis Garicano) 124 9.Fear Pitch 151 10.From Argentina without Emotions 164 11.Discrimination: From the Makana Football Association to Europe 174 Acknowledgments 193 References 195 Index 205

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Book SynopsisFocuses on the difficult question of existence of Frchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. This book provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions.Trade Review"The book is well written--as one would expect from its distinguished authors, including the late Joram Lindestrauss (1936-2012). It contains many fascinating and profound results. It no doubt will become an important resource for anyone who is seriously interested in the differentiability of functions between Banach spaces."--J. Borwein and Liangjin Yao, Mathematical Reviews Clippings "[T]his is a very deep and complete study on the differentiability of Lipschitz mappings between Banach spaces, an unavoidable reference for anyone seriously interested in this topic."--Daniel Azagra, European Mathematical Society "We should be grateful to (the late) Joram Lindenstrauss, David Preiss, and Jaroslav Tiser for providing us with this splendid book which dives into the deepest fields of functional analysis, where the basic but still strange operation called differentiation is investigated. More than a century after Lebesgue, our understanding is not complete. But thanks to the contribution of these three authors, and thanks to this book, we know a fair share of beautiful theorems and challenging problems."--Gilles Godefroy, Bulletin of the American Mathematical SocietyTable of Contents*FrontMatter, pg. i*Contents, pg. vii*Chapter One: Introduction, pg. 1*Chapter Two: Gateaux differentiability of Lipschitz functions, pg. 12*Chapter Three: Smoothness, convexity, porosity, and separable determination, pg. 23*Chapter Four: epsilon-Frechet differentiability, pg. 46*Chapter Five: GAMMA-null and GAMMAn-null sets, pg. 72*Chapter Six: Ferchet differentiability except for GAMMA-null sets, pg. 96*Chapter Seven: Variational principles, pg. 120*Chapter Eight: Smoothness and asymptotic smoothness, pg. 133*Chapter Nine: Preliminaries to main results, pg. 156*Chapter Ten: Porosity, GAMMAn- and GAMMA-null sets, pg. 169*Chapter Eleven: Porosity and epsilon-Frechet differentiability, pg. 202*Chapter Twelve: Frechet differentiability of real-valued functions, pg. 222*Chapter Thirteen: Frechet differentiability of vector-valued functions, pg. 262*Chapter Fourteen: Unavoidable porous sets and nondifferentiable maps, pg. 319*Chapter Fifteen: Asymptotic Frechet differentiability, pg. 355*Chapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces, pg. 392*Bibliography, pg. 415*Index, pg. 419*Index of Notation, pg. 423

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Book SynopsisWhy do humans, uniquely among animals, cooperate in large numbers to advance projects for the common good? Contrary to the conventional wisdom in biology and economics, this generous and civic-minded behavior is widespread and cannot be explained simply by far-sighted self-interest or a desire to help close genealogical kin. In A Cooperative SpecieTrade Review"The achievement of Bowles and Gintis is to have put together from the many disparate sources of evidence a story as plausible as any we're likely to get in the present state of behavioural sciences of how human beings came to be as co-operative as they are."--W.G. Runciman, London Review of Books "In A Cooperative Species, economists Samuel Bowles and Herbert Gintis update their ideas on the evolutionary origins of altruism. Containing new data and analysis, their book is a sustained and detailed argument for how genes and culture have together shaped our ability to cooperate... By presenting clear models that are tied tightly to empirically derived parameters, Bowles and Gintis encourage much-needed debate on the origins of human cooperation."--Peter Richerson, Nature "An outstanding book that presents an important contribution and quite simply raises the scientific standard associated with the difficult and contentious problem of how human altruism evolved."--Charles Efferson, Economic Journal "A Cooperative Species: Human Reciprocity and Its Evolution states a clearly articulated gene-culture coevolution explanation for why we are a cooperative species. It is a read that will stretch readers' minds a bit, and I think it is an eminently valuable read... I await with eagerness the next time Bowles and Gintis are out cooperating again."--Jonathan D. Springer, PsycCRITIQUES "[T]he authors' systematic and mathematical approach will appeal to any reader seriously interested in learning about alternative theories of adaptive altruism, and their treatment of cultural inheritance using population-genetic models is first-rate. Although this book will by no means settle the debate surrounding the evolutionary origin of altruism, it is a worthy addition and is well worth reading."--P. William Hughes, Journal of Economic Issues "Bowles and Gintis are clearly not short of ideas. The attention they draw to the role of conflict and coordinated punishment in the evolution of our cooperative and reciprocal species makes the book very much worth reading. Their focus on the evolution of human nature also paints a much richer picture of our behavior than traditional economics tends to do."--Journal of Economic Literature "Bowles and Gintis are not the first to claim that competition, conflict, and war between human groups is the foundation of cooperation and of society. However, their integration of this insight into evolutionary game theory stands to increase the accessibility of this powerful idea to a large number of scholars working in a dominant theoretical perspective that spans the social and biological sciences. This is one reason why I recommend their new book A Cooperative Species: Human Reciprocity and Its Evolution."--Noah Mark, Journal of Artificial Societies and Social Simulation "This book makes a strong case for returning as a discipline to this vexed theme. I can only hope we do so with the analytical ingenuity and empirical humility that Bowles and Gintis display."--Jacob G. Foster, American Journal of Sociology "Cooperative Species: Human Reciprocity and Its Evolution should be of interest to individuals across multiple disciplines. The book provides a compelling argument supported by multiple kinds of theoretical and empirical evidence. Although the book does use some technical language and examples in places, the explanation is sufficiently clear to make the main ideas and arguments of the book accessible to individuals who were not previously familiar with these technicalities."--Christopher M. Caldwell, Metapsychology Online "[This book] makes important contributions to our understanding of the nature and function of emotions in politics, including the evolution of emotion and cognition and their linkages to democratic governance... [It] should become [an] important resource for students of politics who have the requisite background in the behavioral sciences and wish to develop an integrated, life science perspective in their own work."--Michael S. Latner, Politics and the Life SciencesTable of ContentsPreface xi Chapter 1: A Cooperative Species 1 Chapter 2: The Evolution of Altruism in Humans 8 2.1 Preferences, Beliefs, and Constraints 9 2.2 Social Preferences and Social Dilemmas 10 2.3 Genes, Culture, Groups, and Institutions 13 2.4 Preview 18 Chapter 3: Social Preferences 19 3.1 Strong Reciprocity Is Common 20 3.2 Free-Riders Undermine Cooperation 22 3.3 Altruistic Punishment Sustains Cooperation 24 3.4 Effective Punishment Depends on Legitimacy 26 3.5 Purely Symbolic Punishment Is Effective 29 3.6 People Punish Those Who Hurt Others 31 3.7 Social Preferences Are Not Irrational 32 3.8 Culture and InstitutionsMatter 33 3.9 Behavior Is Conditioned on Group Membership 35 3.10 People Enjoy Cooperating and Punishing Free-Riders 38 3.11 Social Preferences in Laboratory and Natural Settings 39 3.12 Competing Explanations 42 Chapter 4: The Sociobiology of Human Cooperation 46 4.1 Inclusive Fitness and Human Cooperation 48 4.2 Modeling Multi-level Selection 52 4.3 EquilibriumSelection 57 4.4 Reciprocal Altruism 59 4.5 Reciprocal Altruism in Large Groups 63 4.6 Reputation: Indirect Reciprocity 68 4.7 Altruism as a Signal of Quality 71 4.8 Positive Assortment 72 4.9 Mechanisms and Motives 75 Chapter 5: Cooperative Homo economicus 79 5.1 Folk Theorems and Evolutionary Dynamics 80 5.2 The Folk Theorem with Imperfect Public Information 83 5.3 The Folk Theorem with Private Information 86 5.4 Evolutionarily Irrelevant Equilibria 87 5.5 Social Norms and Correlated Equilibria 89 5.6 The Missing Choreographer 90 Chapter 6: Ancestral Human Society 93 6.1 Cosmopolitan Ancestors 95 6.2 Genetic Evidence 99 6.3 PrehistoricWarfare 102 6.4 The Foundations of Social Order 106 6.5 The Crucible of Cooperation 110 Chapter 7: The Coevolution of Institutions and Behaviors 111 7.1 Selective Extinction 115 7.2 Reproductive Leveling 117 7.3 Genetic Differentiation between Groups 120 7.4 Deme Extinction and the Evolution of Altruism 121 7.5 The Australian Laboratory 123 7.6 The Coevolution of Institutions and Altruism 124 7.7 Simulating Gene-Culture Coevolution 126 7.8 Levelers and Warriors 130 Chapter 8: Parochialism, Altruism, andWar 133 8.1 Parochial Altruism and War 135 8.2 The Emergence of Parochial Altruism and War 138 8.3 Simulated and Experimental Parochial Altruism 142 8.4 The Legacy of a Past "Red in Tooth and Claw" 146 Chapter 9: The Evolution of Strong Reciprocity 148 9.1 Coordinated Punishment 150 9.2 Altruistic Punishment in a Realistic Demography 156 9.3 The Emergence of Strong Reciprocity 159 9.4 Why Coordinated Punishment Succeeds 163 9.5 A Decentralized Social Order 164 Chapter 10: Socialization 167 10.1 Cultural Transmission 168 10.2 Socialization and the Survival of Fitness-Reducing Norms 171 10.3 Genes, Culture, and the Internalization of Norms 173 10.4 The Internalized Norm as Hitchhiker 176 10.5 The Gene-Culture Coevolution of a Fitness-Reducing Norm 179 10.6 How Can Internalized Norms Be Altruistic? 180 10.7 The Programmable Brain 183 11Social Emotions 186 11.1 Reciprocity, Shame, and Punishment 188 11.2 The Evolution of Social Emotions 191 11.3 The "Great Captains of Our Lives" 192 12Conclusion: Human Cooperation and Its Evolution 195 12.1 The Origins of Human Cooperation 196 12.2 The Future of Cooperation 199 Appendix 201 A1 Altruism Defined 201 A2 Agent-Based Models 202 A3 Game Theory 207 A4 Dynamical Systems 209 A5 The Replicator Dynamic 212 A6 Continuation Probability and Time Discount Factor 213 A7 Alternatives to the Standing Model 214 A8 The Prisoner's Dilemma with Public and Private Signals 215 A9 Student and Nonstudent Experimental Subjects 217 A10 The Price Equation 218 A11 Weak Multi-level Selection 222 A12 Cooperation and Punishment with Quorum Sensing 223 References 225 Subject Index 251 Author Index 255

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Book SynopsisGame Theory in Action is a textbook about using game theory across a range of real-life scenarios. From traffic accidents to the sex lives of lizards, Stephen Schecter and Herbert Gintis show students how game theory can be applied in diverse areas including animal behavior, political science, and economics. The book's examples and problems look aTrade Review"Though not an advanced treatment mathematically speaking, readers become sophisticated consumers of game theories."--Choice "A welcome addition to the existing collection of introductory game theory texts... A very satisfying book."--Jennifer M. Wilson, MathSciNet "[A] wonderful introduction to game theory... I found almost all the games and examples fun to read and fun to work through the decisions and matrices. Whether the games were about politics, wine merchants and connoisseurs, or simply how to view sex ratios in society, you will find something of interest in this book."--David S. Mazel, MAA ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface and acknowledgments, pg. xi*Chapter 1. Backward induction, pg. 1*Chapter 2. Eliminating dominated strategies, pg. 37*Chapter 3. Nash equilibria, pg. 61*Chapter 4. Games in extensive form with incomplete information, pg. 88*Chapter 5. Mixed strategy Nash equilibria, pg. 114*Chapter 5. Mixed strategy Nash equilibria, pg. 151*Chapter 7. Symmetries of games, pg. 186*Chapter 8. Alternatives to the Nash equilibrium, pg. 203*Chapter 9. Differential equations, pg. 217*Chapter 10. Evolutionary dynamics, pg. 232*Appendix. Sources for examples and problems, pg. 265*References, pg. 269*Index, pg. 271

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Book SynopsisGame Theory in Action is a textbook about using game theory across a range of real-life scenarios. From traffic accidents to the sex lives of lizards, Stephen Schecter and Herbert Gintis show students how game theory can be applied in diverse areas including animal behavior, political science, and economics. The book's examples and problems look aTrade Review"Though not an advanced treatment mathematically speaking, readers become sophisticated consumers of game theories."--Choice "A welcome addition to the existing collection of introductory game theory texts... A very satisfying book."--Jennifer M. Wilson, MathSciNet "[A] wonderful introduction to game theory... I found almost all the games and examples fun to read and fun to work through the decisions and matrices. Whether the games were about politics, wine merchants and connoisseurs, or simply how to view sex ratios in society, you will find something of interest in this book."--David S. Mazel, MAA ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface and acknowledgments, pg. xi*Chapter 1. Backward induction, pg. 1*Chapter 2. Eliminating dominated strategies, pg. 37*Chapter 3. Nash equilibria, pg. 61*Chapter 4. Games in extensive form with incomplete information, pg. 88*Chapter 5. Mixed strategy Nash equilibria, pg. 114*Chapter 5. Mixed strategy Nash equilibria, pg. 151*Chapter 7. Symmetries of games, pg. 186*Chapter 8. Alternatives to the Nash equilibrium, pg. 203*Chapter 9. Differential equations, pg. 217*Chapter 10. Evolutionary dynamics, pg. 232*Appendix. Sources for examples and problems, pg. 265*References, pg. 269*Index, pg. 271

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Book SynopsisTrade Review"Noncooperative Game Theory offers students a fresh way of approaching engineering and computer science applications." * Mathematical Reviews *Table of ContentsPreamble xi I INTRODUCTION 1 Noncooperative Games 1.1 Elements of a Game 3 1.2 Cooperative vs. Noncooperative Games: Rope-Pulling 4 1.3 Robust Designs: Resistive Circuit 8 1.4 Mixed Policies: Network Routing 9 1.5 Nash Equilibrium 11 1.6 Practice Exercise 11 2 Policies 2.1 Actions vs. Policies: Advertising Campaign 13 2.2 Multi-Stage Games:War of Attrition 16 2.3 Open vs. Closed-Loop: Zebra in the Lake 18 2.4 Practice Exercises 19 II ZERO-SUM GAMES 3 Zero-Sum Matrix Games 3.1 Zero-Sum Matrix Games 25 3.2 Security Levels and Policies 26 3.3 Computing Security Levels and Policies with MATLAB(R) 27 3.4 Security vs. Regret: Alternate Play 28 3.5 Security vs. Regret: Simultaneous Plays 28 3.6 Saddle-Point Equilibrium 29 3.7 Saddle-Point Equilibrium vs. Security Levels 30 3.8 Order Interchangeability 32 3.9 Computational Complexity 32 3.10 Practice Exercise 34 3.11 Additional Exercise 34 4 Mixed Policies 4.1 Mixed Policies: Rock-Paper-Scissor 35 4.2 Mixed Action Spaces 37 4.3 Mixed Security Policies and Saddle-Point Equilibrium 38 4.4 Mixed Saddle-Point Equilibrium vs. Average Security Levels 41 4.5 General Zero-Sum Games 43 4.6 Practice Exercises 47 4.7 Additional Exercise 50 5 Minimax Theorem 5.1 Theorem Statement 52 5.2 Convex Hull 53 5.3 Separating Hyperplane Theorem 54 5.4 On theWay to Prove the Minimax Theorem 55 5.5 Proof of the Minimax Theorem 57 5.6 Consequences of the Minimax Theorem 58 5.7 Practice Exercise 58 6 Computation of Mixed Saddle-Point Equilibrium Policies 6.1 Graphical Method 60 6.2 Linear Program Solution 61 6.3 Linear Programs with MATLAB(R) 63 6.4 Strictly Dominating Policies 64 6.5 "Weakly" Dominating Policies 66 6.6 Practice Exercises 67 6.7 Additional Exercise 70 7 Games in Extensive Form 7.1 Motivation 71 7.2 Extensive Form Representation 72 7.3 Multi-Stage Games 72 7.4 Pure Policies and Saddle-Point Equilibria 74 7.5 Matrix Form for Games in Extensive Form 75 7.6 Recursive Computation of Equilibria for Single-Stage Games 77 7.7 Feedback Games 79 7.8 Feedback Saddle-Point for Multi-Stage Games 79 7.9 Recursive Computation of Equilibria for Multi-Stage Games 83 7.10 Practice Exercise 85 7.11 Additional Exercises 86 8 Stochastic Policies for Games in Extensive Form 8.1 Mixed Policies and Saddle-Point Equilibria 87 8.2 Behavioral Policies for Games in Extensive Form 90 8.3 Behavioral Saddle-Point Equilibria 91 8.4 Behavioral vs. Mixed Policies 92 8.5 Recursive Computation of Equilibria for Feedback Games 93 8.6 Mixed vs. Behavioral Order Interchangeability 95 8.7 Non-Feedback Games 95 8.8 Practice Exercises 96 8.9 Additional Exercises 102 III NON-ZERO-SUM GAMES 9 Two-Player Non-Zero-Sum Games 9.1 Security Policies and Nash Equilibria 105 9.2 Bimatrix Games 107 9.3 Admissible Nash Equilibria 108 9.4 Mixed Policies 110 9.5 Best-Response Equivalent Games and Order Interchangeability 111 9.6 Practice Exercises 114 9.7 Additional Exercises 116 10 Computation of Nash Equilibria for Bimatrix Games 10.1 Completely Mixed Nash Equilibria 118 10.2 Computation of Completely Mixed Nash Equilibria 120 10.3 Numerical Computation of Mixed Nash Equilibria 121 10.4 Practice Exercise 124 10.5 Additional Exercise 126 11 N-Player Games 11.1 N-Player Games 127 11.2 Pure N-Player Games in Normal Form 129 11.3 Mixed Policies for N-Player Games in Normal Form 130 11.4 Completely Mixed Policies 131 12 Potential Games 12.1 Identical Interests Games 133 12.2 Potential Games 135 12.3 Characterization of Potential Games 138 12.4 Potential Games with Interval Action Spaces 139 12.5 Practice Exercises 142 12.6 Additional Exercise 144 13 Classes of Potential Games 13.1 Identical Interests Plus Dummy Games 145 13.2 Decoupled Plus Dummy Games 146 13.3 Bilateral Symmetric Games 147 13.4 Congestion Games 148 13.5 Other Potential Games 149 13.6 Distributed Resource Allocation 150 13.7 Computation of Nash Equilibria for Potential Games 153 13.8 Fictitious Play 156 13.9 Practice Exercises 159 13.10 Additional Exercises 167 IV DYNAMIC GAMES 14 Dynamic Games 14.1 Game Dynamics 171 14.2 Information Structures 173 14.3 Continuous-Time Differential Games 175 14.4 Differential Games with Variable Termination Time 177 15 One-Player Dynamic Games 15.1 One-Player Discrete-Time Games 178 15.2 Discrete-Time Cost-To-Go 179 15.3 Discrete-Time Dynamic Programming 179 15.4 Computational Complexity 184 15.5 Solving Finite One-Player Games with MATLAB(R) 186 15.6 Linear Quadratic Dynamic Games 187 15.7 Practice Exercise 187 15.8 Additional Exercise 189 16 One-Player Differential Games 16.1 One-Player Continuous-Time Differential Games 190 16.2 Continuous-Time Cost-To-Go 191 16.3 Continuous-Time Dynamic Programming 191 16.4 Linear Quadratic Dynamic Games 195 16.5 Differential Games with Variable Termination Time 196 16.6 Practice Exercise 198 17 State-Feedback Zero-Sum Dynamic Games 17.1 Zero-Sum Dynamic Games in Discrete Time 201 17.2 Discrete-Time Dynamic Programming 203 17.3 Solving Finite Zero-Sum Games with MATLAB(R) 205 17.4 Linear Quadratic Dynamic Games 206 17.5 Practice Exercise 209 18 State-Feedback Zero-Sum Differential Games 18.1 Zero-Sum Dynamic Games in Continuous Time 214 18.2 Linear Quadratic Dynamic Games 216 18.3 Differential Games with Variable Termination Time 219 18.4 Pursuit-Evasion 220 18.5 Practice Exercise 222 References 223 Index 225

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Book SynopsisTrade Review“Charlie Holt has been at the very forefront in bringing experiments into the mainstream of economic research and, especially, in using experiments to teach economics. This book will give undergraduates or masters students a chance to learn from a pioneering experimenter and a master teacher.”—Alvin Roth, Stanford University “This is a great book for teaching undergraduates, covering a host of topics from which teachers can choose, and including experiments to do in class. Charles Holt, one of the pioneers of experimental economics, is a clear thinker and a great expositor. There are no competitors to this book.”—Guillaume R. Fréchette, New York University“Charles Holt is one of the founders of experimental economics and he has contributed to nearly every one of its subfields. This is an excellent book and there are no viable competing texts for undergraduate experimental economics.”—Charles Noussair, University of Arizona

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Book Synopsis

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Book SynopsisMathematicians Playing Games explores a wide variety of popular mathematical games, including their historical beginnings and the mathematical theories that underpin them. Its academic level is suitable for high school students and higher, but people of any age or level will find something to entertain them, and something new to learn. It would be a fantastic resource for high school mathematics classrooms or undergraduate mathematics for liberal arts course and belongs on the shelf of anyone with an interest in recreational mathematics.Features Suitable for anyone with an interest in games and mathematics, and could be especially useful to middle and high school students and their teachers Includes various exercises for fun for readers Table of Contents1. 15 Puzzle: A Tile Matching Game That Is Difficult Even for Computers.2. Peg Solitaire: Jumping Game Where We Meet Algebra.3. Chomp Game: Avoid a Poisoned Chocolate.4. Super Tic-Tac-Toe: Stone Game over a Donut.5. Mastermind: A Cryptographic Game.6. Ramsey Theorem and Sim Game: Don’t Draw a Red Triangle.7. Nine Men’s Morris: Three Soldiers' Side by Side.8. The Game of Quatrainment: Flip Neighbor Stones.9. n-Queens Game and Puzzle: Playing Chess Only with Queens.10. Light Out: Turn Off Lights by Linear Equations.11. 1258 Board Game: Magic Square and Orthogonal Latin Square.12. Switching Game: Shannon’s Network Game.13. Dots and Boxes: Occupy More Boxes.14. Matricking: Factorization and Cube Net Game.15. SET Game: Steiner Triple System Game.16. Dobble Game: Finite Projective Plane Game.17. Find-a-Best-Friend Game: A Game of the Perfect Hamming Code.

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Book SynopsisIn this 2005 book, many topics in natural selection are investigated including co-evolution, speciation, and extinction. It may be described as a book on mathematical Darwinism. Darwin used logical verbal arguments to understand evolution. These arguments are presented here in a mathematical setting useful for both understanding evolution and allowing for prediction as well.Trade ReviewReview of the hardback: 'It's complicated, but it's where biology is at, and Vincent and Brown clarify the issues wonderfully.' BiologistReview of the hardback: '… even-handedness, together with its peerless reasoning, helps this book stand out in a crowded field … masterly book. … time and again, Shanahan convinces us that Darwin's approach was relentlessly reconciliatory, pluralistic, and non dogmatic … Because it is equally ardent and articulate, Shanahan's own relentlessly moderate voice is likely to survive the fashionable Sturn und Drang.' Journal of the History of the Behavioral SciencesReview of the hardback: '… provides a formal game-theoretic framework for addressing an impressive array of biological questions.' Journal of Mammalian EvolutionReview of the hardback: 'The book is written in an enthusiastic style. In several places you can still perceive the excitement the authors must have felt when they embarked on their work in evolutionary dynamics … a must-read for those interested in the history of evolutionary game theory …' www.PalArch.nlTable of Contents1. Understanding natural selection; 2. Underlying mathematics and philosophy; 3. The Darwinian game; 4. G-functions for the Darwinian game; 5. Darwinian dynamics; 6. Evolutionary stable strategies; 7. The ESS maximum principle; 8. Speciation and extinction; 9. Matrix games; 10. Evolutionary ecology; 11. Managing evolving systems.

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Book SynopsisPolitical Game Theory is a self-contained introduction to game theory and its applications to political science. The methods employed have many applications in various disciplines including comparative politics, international relations and American politics. A large number of exercises are also provided to practice the skills and techniques discussed.Trade Review"At last, a challenging but accessible graduate-level text for a serious course in game theory for political scientists. Teaching game theory in the context of political-science examples, this book will be the standard text for many years to come." Robert Powell, BerkeleyTable of Contents1. Introduction; 2. The theory of choice; 3. Choice under uncertainty; 4. Social choice theory; 5. Games in the normal form; 6. Bayesian games in the normal form; 7. Extensive form games; 8. Dynamic games of incomplete information; 9. Repeated games; 10. Bargaining theory; 11. Mechanism design and agency theory; 12. Mathematical appendix.

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Book SynopsisFor advanced students in economics, this textbook provides a clear and concise introduction to dynamic economic theory and analysis. Sorger guides students step-by-step through the most popular model structures and solution concepts, from the simplest dynamic economic models to complex problems of dynamic general equilibrium frameworks.Trade Review'This book offers a comprehensive vision of economic dynamics suitable for graduate students and professionals alike. Gerhard Sorger is a leading researcher with a flair for presenting mathematically challenging theories carefully and rigorously. His text emphasizes the interplay between formal theory and applications with detailed developments of a catalogue of economic models and examples drawn from macroeconomics, growth theory and game theory. There is no other single book readily accessible in the economics literature covering the same wide range of deterministic dynamics and optimization theories with detailed illustrations of those theories in action. It is accessible to students engaged in a self-study program for students engaging with dynamical systems for the first time. Better yet, it offers the topics and treatments for a course in dynamics.' Robert A. Becker, Indiana University, Bloomington'This is a beautifully written book, providing a completely self-contained introduction to dynamic economic methods and models for graduate students in economics. The masterly exposition strikes a perfect balance between a user-friendly approach and a completely rigorous presentation of the subject matter. The style of writing is marked by exceptional clarity, very much in keeping with the high standards set by the author in his research contributions. The book is neatly divided into two parts, the first providing a comprehensive account of the theory of dynamical systems, and the second the theory and applications of dynamic optimization in settings with single and multiple decision makers. The chapters on Autonomous Difference Equations and Optimization Techniques are real gems, and should form the core material in any course on dynamic economic analysis.' Tapan Mitra, Goldwin Smith Professor of Economics, Cornell University'Up to now, there are very few books available at the graduate level that introduce the necessary mathematical techniques to study macroeconomics from the viewpoint of nonlinear dynamics. Gerhard Sorger is one of the few theorists who have made profound contributions to the subject. His book beautifully introduces the basic results and synthesizes the latest developments in the discrete time nonlinear growth models. This book is ideally suited as a textbook for graduate courses in macroeconomics and mathematical economics. Gerhard Sorger should be congratulated on his efforts to educate young researchers. I highly recommend this book.' Kazuo Nishimura, RIEB, Kobe UniversityTable of ContentsPreface; Part I. Difference Equations: 1. Basic concepts; 2. Linear difference equations; 3. Autonomous difference equations; 4. One-dimensional maps; Part II. Dynamic Optimization: 5. Optimization techniques; 6. Dynamic inconsistency and commitment; 7. Dynamic games; 8. Dynamic competitive equilibrium; References; Index.

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Book SynopsisThis book explores the creation of game theory by John von Neumann and Oskar Morgenstern. A dramatic reconstruction shows how game theory was related to debates in economics and mathematics, the social and political upheaval of the period, and the dramatic personal histories of its two architects.Trade Review'Robert Leonard toiled for more than a decade on his manuscript on the creators and creation of game theory. His nuanced account is 'thick history' at its best; he captures the protagonists and their milieu with precision and flair. It is a signal achievement.' Bruce Caldwell, Duke University'The publication of Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern in 1944 was hailed by one reviewer as 'one of the major scientific achievements of the first half of the twentieth century'. In this exemplary study in the history of economics, Robert Leonard has given us a masterful account of the gestation of this work, starting with the importance of chess in European intellectual life at the beginning of the twentieth century and ending with the military applications of game theory at the RAND Corporation during the middle of the century. Leonard has given us absorbing parallel biographies of von Neumann and Morgenstern, while painting a fascinating background of the Hungarian mathematical scene and the Viennese economic world. Every practitioner of game theory and every student of twentieth-century intellectual history should read this book.' Harold W. Kuhn, Princeton University'Robert Leonard excavates a multifarious genealogy for John von Neumann and Oskar Morgenstern's pioneering Theory of Games and Economic Behavior across a landscape that features some of the early twentieth century's key sites of mathematical aspiration, economic disputation, and political and personal tragedy.' Ted Porter, University of California, Los Angeles'This fine book provides a rich context for the understanding of the Austrian school of economics together with the mathematics of Hungary, Germany, and elsewhere that culminated in the theory of games. It is the product of many years of scholarship and presents much information basically unknown to those who came to game theory after the 1940s.' Martin Shubik, Journal of Economic Literature'Leonard unpacks the contributions of developments in psychology, philosophy, mathematics, economics, and politics to the origins of game theory. He shows how external events - the rise of Nazism, World War II, and the beginning of the Cold War - interacted with the personalities of von Neumann and Morgenstern and their successors to shape the development of the theory itself and the unanticipated uses to which it has been put. The result is a book that combines the rigor of a textbook with the excitement of a historical novel.' Marina von Neumann Whitman, University of Michigan'Leonard's masterful fresco follows the development of game theory from its prelude in turn-of-the-century Vienna chess cafes and the mathematical circles of Hungary to its multifarious first steps in the writings of Borel and Zermelo …' Giacomo Sillari, History of Economic Thought and Policy'Von Neumann and Morgenstern's landmark 1944 book, Theory of Games and Economic Behavior, has long proven enigmatic. As is well known, the book's immediate impact on economic theory was minor, yet it has been widely cited as the inspiration for game theory as it has infiltrated economics since the 1980s … What is clear is that [this] book represents immense achievement in the way it links the histories of science, economics, and cultural and social history through the early careers of John von Neumann and Oskar Morgenstern. To a broader audience, its attention to social and political context will make parts of the book read like a page-turner, while it will remain a rich resource for the scholarly initiate.' Journal of Economics and PhilosophyTable of ContentsIntroduction; Part I. Struggle and Equilibrium: From Lasker to von Neumann: 1. 'The strangest states of mind': chess, psychology and Emanuel Lasker's Kampf; 2. 'Deeply rooted yet alien': Hungarian Jews and mathematicians; 3. From Budapest to Göttingen: an apprenticeship in modern mathematics; 4. 'The futile search for the perfect formula': von Neumann's minimax theorem; Part II. Oskar Morgenstern and Interwar Vienna: 5. Equilibrium on trial: the young Morgenstern and the Austrian school; 6. Wrestling with complexity: Wirtschaftsprognose and beyond; 7. Ethics and the excluded middle: Karl Menger and social science; 8. From Austroliberalism to Anschluss: the Viennese economists in the 1930s; Part III. From War to Cold War: 9. Mathematics and the social order: von Neumann's return to game theory; 10. Ars combinatoria: writing the theory of games; 11. Morgenstern's catharsis; 12. Von Neumann's war; 13. Social science and the 'present danger': game theory and psychology at the RAND Corporation, 1946–60; Conclusion.

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Book SynopsisThe appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.Trade Review'One of the wellsprings out of which the discipline of mathematics has developed is human delight in intellectual play, manifest in the ubiquity of abstract games across millennia and cultures. The author of this fascinating book is expert in both domains, and in the art of clearly explaining significant aspects of mathematics in ways both accessible to non-experts and illuminating to experts. Through a delightfully rich variety of historical and multicultural examples, he unveils the intimate relationship between abstract games and mathematics as the study of structures, and, in so doing, illuminates much more about mathematical behaviour and cognition. At a time when too much of mathematics education in school seems designed to squeeze out every last drop of playfulness, we are reminded that mathematics can, and should, be an intellectual playground.' Brian Greer, Portland State University'This is a very approachable yet erudite book. Wells' game is to turn Plato's theory of forms on its head: instead of starting with physical examples and imagining their ideal forms, we should take our cue from the abstract laws and intuitions of games. Chess pieces are defined by their powers rather than their physical forms, and so are many situations in mathematics … The book illustrates this thesis with fascinating context: from Ulam's 'lucky' numbers … to the symmetry of the theorem discovered by Emperor Napoleon and the mathematics which arises in Go, Hex and chess … Games and Mathematics makes an important advance in communicating the nature of mathematics. It contains a profound message for philosophers of mathematics, but all mathematically-inclined readers will find [it] as compelling as Wells' excellent 'Curious and Interesting' books.' Paul Brown, author of Proof: Interesting Activities in Conjecture and Mathematical Proof'This is no ordinary compilation of recreational problems in mathematics … the text reads well and is something of a page-turner … this is not a mere compilation of problems, but a guided tour, and one would hope that it would reach a wider audience, so the authors' expressed intention, of showing that mathematics is not merely computation, but actually foremost an imaginative play, should become effective … All in all this could be a delightful volume in every aspect and I find myself recommending the work … with warmth and enthusiasm and with no qualms.' Ulf Persson, Chalmers University of Technology, Gothenburg'Complete with a consistent argument and a wealth of supportive references, this is a fun work for both game players and mathematicians to explore. Highly recommended.' J. Johnson, ChoiceTable of ContentsIntroduction; Part I. Mathematical recreations and abstract games: 1. Recreations from Euler to Lucas; 2. Four abstract games; 3. Mathematics and games: mysterious connections; 4. Why chess is not mathematics; 5. Proving versus checking; Part II. Mathematics: game-like, scientific and perceptual: 6. Game-like mathematics; 7. Euclid and the rules of his geometrical game; 8. New concepts and new objects; 9. Convergent and divergent series; 10. Mathematics becomes game-like; 11. Maths as science; 12. Numbers and sequences; 13. Computers and mathematics; 14. Mathematics and the sciences; 15. Minimum paths from Heron to Feynmann; 16. The foundations: perception, imagination and insight; 17. Structure; 18. Hidden structure, common structure; 19. Mathematics and beauty; 20. Origins: formality in the everyday world; Bibliography; Index.

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Book SynopsisEdited by several of the leading figures in the field, this is the first book to provide a state-of-the-art, accessibly written methodological introduction to the tools and techniques of agent-based modelling. Using these building blocks, readers will learn how to design, simulate, and validate agent-based models in economics.Trade Review'Some 25 years ago, Frank Hahn a leading economic theorist said, '… wildly complex systems need simulating … while there will be work for the computer scientist, I very much doubt that economists will be able to establish general propositions in any but very special examples'. Economists have reacted by saying 'show us an alternative'. This book does just that. It provides the elements of an alternative computational approach in which aggregate phenomena such as crises do not appear from the blue, but emerge from the interaction between simple but heterogeneous agents.' Alan Kirman, University of Aix-Marseille III'The authors conceive of economies as complex systems of heterogeneous interacting agents with bounded rationality and limited information, and they view agent-based modeling as a necessary tool for the exploration of such systems. In this book the authors provide a comprehensive introduction to agent-based modeling. Although macroeconomic applications are stressed, the coverage of topics such as rationality, behavior, expectations, and learning will be of value for many other applications as well. A particularly welcome aspect of the book is its attention to historical antecedents and its inclusion of chapters devoted to empirical validation and estimation issues.' Leigh Tesfatsion, Iowa State UniversityTable of Contents1. Introduction; 2. Agent-based computational economics: what, why, when; 3. Agent-based models as recursive systems; 4. Rationality, behaviour and expectations; 5. Agents' behaviour and learning; 6. Interaction; 7. The agent-based experiment; 8. Empirical validation of agent-based models; 9. Estimation of agent-based models; 10. Epilogue.

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Book SynopsisNow in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual for instructors with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reTrade ReviewPraise for first edition: 'This is the book for which the world has been waiting for decades: a definitive, comprehensive account of the mathematical theory of games, by three of the world's biggest experts on the subject. Rigorous yet eminently readable, deep yet comprehensible, replete with a large variety of important real-world applications, it will remain the standard reference in game theory for a very long time.' Robert Aumann, Nobel Laureate in Economics, The Hebrew University of JerusalemPraise for first edition: 'Without any sacrifice on the depth or the clarity of the exposition, this book is amazing in its breadth of coverage of the important ideas of game theory. It covers classical game theory, including utility theory, equilibrium refinements and belief hierarchies; classical cooperative game theory, including the core, Shapley value, bargaining set and nucleolus; major applications, including social choice, auctions, matching and mechanism design; and the relevant mathematics of linear programming and fixed point theory. The comprehensive coverage combined with the depth and clarity of exposition makes it an ideal book not only to learn game theory from, but also to have on the shelves of working game theorists.' Ehud Kalai, Kellogg School of Management, Northwestern UniversityPraise for first edition: 'The best and the most comprehensive textbook for advanced courses in game theory.' David Schmeidler, Ohio State University and Tel Aviv UniversityPraise for first edition: 'There are quite a few good textbooks on game theory now, but for rigor and breadth this one stands out.' Eric S. Maskin, Nobel Laureate in Economics, Harvard University, MassachusettsPraise for first edition: 'This textbook provides an exceptionally clear and comprehensive introduction to both cooperative and noncooperative game theory. It deftly combines a rigorous exposition of the key mathematical results with a wealth of illuminating examples drawn from a wide range of subjects. It is a tour de force.' Peyton Young, University of OxfordPraise for first edition: 'This is a wonderful introduction to game theory, written in a way that allows it to serve both as a text for a course and as a reference … The book is written by leading figures in the field [whose] broad view of the field suffuses the material.' Joe Halpern, Cornell University, New YorkTable of Contents1. The game of chess; 2. Utility theory; 3. Extensive-form games; 4. Strategic-form games; 5. Mixed strategies; 6. Behavior strategies and Kuhn's theorem; 7. Equilibrium refinements; 8. Correlated equilibria; 9. Games with incomplete information and common priors; 10. Games with incomplete information: the general model; 11. The universal belief space; 12. Auctions; 13. Repeated games; 14. Repeated games with vector payoffs; 15. Social choice; 16. Bargaining games; 17. Coalitional games with transferable utility; 18. The core; 19. The Shapley value; 20. The bargaining set; 21. The nucleolus; 22. Stable matching; 23. Appendices.

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Book SynopsisDifferential Game Theory with Applications to Missiles and Autonomous Systems explains the use of differential game theory in autonomous guidance and control systems. The book begins with an introduction to the basic principles before considering optimum control and game theory.Table of ContentsPreface xi Acknowledgments xiii About the Companion Website xv 1 Differential Game Theory and Applications to Missile Guidance 1 Nomenclature 1 Abbreviations 2 1.1 Introduction 2 1.1.1 Need for Missile Guidance—Past, Present, and Future 2 1.2 Game Theoretic Concepts and Definitions 3 1.3 Game Theory Problem Examples 4 1.3.1 Prisoner’s Dilemma 4 1.3.2 The Game of Tic-Tac-Toe 6 1.4 Game Theory Concepts Generalized 8 1.4.1 Discrete-Time Game 8 1.4.2 Continuous-Time Differential Game 9 1.5 Differential Game Theory Application to Missile Guidance 10 1.6 Two-Party and Three-Party Pursuit-Evasion Game 11 1.7 Book Chapter Summaries 11 1.7.1 A Note on the Terminology Used In the Book 13 References 14 2 Optimum Control and Differential Game Theory 16 Nomenclature 16 Abbreviations 17 2.1 Introduction 17 2.2 Calculus of Optima (Minimum or Maximum) for a Function 18 2.2.1 On the Existence of the Necessary and Sufficient Conditions for an Optima 18 2.2.2 Steady State Optimum Control Problem with Equality Constraints Utilizing Lagrange Multipliers 19 2.2.3 Steady State Optimum Control Problem for a Linear System with Quadratic Cost Function 22 2.3 Dynamic Optimum Control Problem 23 2.3.1 Optimal Control with Initial and Terminal Conditions Specified 23 2.3.2 Boundary (Transversality) Conditions 25 2.3.3 Sufficient Conditions for Optimality 29 2.3.4 Continuous Optimal Control with Fixed Initial Condition and Unspecified Final Time 30 2.3.5 A Further Property of the Hamiltonian 35 2.3.6 Continuous Optimal Control with Inequality Control Constraints— the Pontryagin’s Minimum (Maximum) Principle 36 2.4 Optimal Control for a Linear Dynamical System 38 2.4.1 The LQPI Problem—Fixed Final Time 38 2.5 Optimal Control Applications in Differential Game Theory 40 2.5.1 Two-Party Game Theoretic Guidance for Linear Dynamical Systems 41 2.5.2 Three-Party Game Theoretic Guidance for Linear Dynamical Systems 44 2.6 Extension of the Differential Game Theory to Multi-Party Engagement 50 2.7 Summary and Conclusions 50 References 51 Appendix 53 3 Differential Game Theory Applied to Two-Party Missile Guidance Problem 63 Nomenclature 63 Abbreviations 64 3.1 Introduction 64 3.2 Development of the Engagement Kinematics Model 67 3.2.1 Relative Engage Kinematics of n Versus m Vehicles 68 3.2.2 Vector/Matrix Representation 69 3.3 Optimum Interceptor/Target Guidance for a Two-Party Game 70 3.3.1 Construction of the Differential Game Performance Index 70 3.3.2 Weighting Matrices S, R p ,R e 72 3.3.3 Solution of the Differential Game Guidance Problem 73 3.4 Solution of the Riccati Differential Equations 75 3.4.1 Solution of the Matrix Riccati Differential Equations (MRDE) 75 3.4.2 State Feedback Guidance Gains 76 3.4.3 Solution of the Vector Riccati Differential Equations (VRDE) 77 3.4.4 Analytical Solution of the VRDE for the Special Case 78 3.4.5 Mechanization of the Game Theoretic Guidance 79 3.5 Extension of the Game Theory to Optimum Guidance 79 3.6 Relationship with the Proportional Navigation (PN) and the Augmented PN Guidance 81 3.7 Conclusions 82 References 82 Appendix 84 4 Three-Party Differential Game Theory Applied to Missile Guidance Problem 102 Nomenclature 102 Abbreviations 103 4.1 Introduction 103 4.2 Engagement Kinematics Model 104 4.2.1 Three-Party Engagement Scenario 105 4.3 Three-Party Differential Game Problem and Solution 107 4.4 Solution of the Riccati Differential Equations 111 4.4.1 Solution of the Matrix Riccati Differential Equation (MRDE) 111 4.4.2 Solution of the Vector Riccati Differential Equation (VRDE) 112 4.4.3 Further Consideration of Performance Index (PI) Weightings 115 4.4.4 Game Termination Criteria and Outcomes 116 4.5 Discussion and Conclusions 116 References 117 Appendix 118 5 Four Degrees-of-Freedom (DOF) Simulation Model for Missile Guidance and Control Systems 125 Nomenclature 125 Abbreviations 126 5.1 Introduction 126 5.2 Development of the Engagement Kinematics Model 126 5.2.1 Translational Kinematics for Multi-Vehicle Engagement 126 5.2.2 Vector/Matrix Representation 128 5.2.3 Rotational Kinematics: Relative Range, Range Rates, Sightline Angles, and Rates 128 5.3 Vehicle Navigation Model 130 5.3.1 Application of Quaternion to Navigation 131 5.4 Vehicle Body Angles and Flight Path Angles 133 5.4.1 Computing Body Rates (p I ,q I ,r I) 134 5.5 Vehicle Autopilot Dynamics 135 5.6 Aerodynamic Considerations 135 5.7 Conventional Guidance Laws 136 5.7.1 Proportional Navigation (PN) Guidance 136 5.7.2 Augmented Proportional Navigation (APN) Guidance 137 5.7.3 Optimum Guidance and Game Theory–Based Guidance 137 5.8 Overall State Space Model 138 5.9 Conclusions 138 References 139 Appendix 140 6 Three-Party Differential Game Missile Guidance Simulation Study 150 Nomenclature 150 Abbreviations 150 6.1 Introduction 151 6.2 Engagement Kinematics Model 151 6.3 Game Theory Problem and the Solution 154 6.4 Discussion of the Simulation Results 157 6.4.1 Game Theory Guidance Demonstrator Simulation 157 6.4.2 Game Theory Guidance Simulation Including Disturbance Inputs 160 6.5 Conclusions 162 6.5.1 Useful Future Studies 162 References 163 Appendix 164 Addendum 165 Index 189

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Book SynopsisThis book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, reflexion in chess, art works, etc. The present book is intended for experts in decision making and control of systems of an interdisciplinary nature, as well as for undergraduates and postgraduates.Table of ContentsIntroduction. 1. Reflexion in decision-making 2. Informational reflexion and control 3. Strategic reflexion and control 4. Applied models of informational and reflexive control. Conclusion.

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Book SynopsisThis book gives students a quick and accessible introduction to many of the most important concepts in the field of algorithmic game theory. It demonstrates these concepts through case studies in online advertising, wireless spectrum auctions, kidney exchange, and network management.Trade Review'There are several features of this book that make it very well suited both for the classroom and for self-study … if your interest is in understanding how game theory, economics and computer science are cross-pollinating to address challenges of the design of online strategic interactions, this is the book to start with. It is clear, well-organized and makes a compelling introduction to a vibrant field.' David Burke, MAA ReviewsTable of Contents1. Introduction and examples; 2. Mechanism design basics; 3. Myerson's Lemma; 4. Algorithmic mechanism design 34; 5. Revenue-maximizing auctions; 6. Simple near-optimal auctions; 7. Multi-parameter mechanism design; 8. Spectrum auctions; 9. Mechanism design with payment constraints; 10. Kidney exchange and stable matching; 11. Selfish routing and the price of anarchy; 12. Network over-provisioning and atomic selfish routing; 13. Equilibria: definitions, examples, and existence; 14. Robust price-of-anarchy bounds in smooth games; 15. Best-case and strong Nash equilibria; 16. Best-response dynamics; 17. No-regret dynamics; 18. Swap regret and the Minimax theorem; 19. Pure Nash equilibria and PLS-completeness; 20. Mixed Nash equilibria and PPAD-completeness.

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Book SynopsisLevel design connects the player to the game through challenges, experiences, and emotions. This book is an invaluable introduction to the evolving practices of Level Designers across the games industry. The increasingly complex role of the Level Designer requires technical and creative skill as it brings together architecture, art, player psychology, interaction design, usability, and experience design. This book explores in detail the principles designers employ when planning levels and building engaging spaces for the player. As well as practical approaches to level design, the book delves into the theoretical underpinnings of the processes and charts a path towards thinking like a Level Designer. Throughout the book you will be guided through the fundamentals of level design: each chapter builds on the types of research, ideation, best practices, and methodologies Level Designers employ when creating prototypes and shipped games. A series of interviews with designers and case studiTrade ReviewA pragmatic approach to level design that captures the critical elements needed to conceptualize and create meaningful player experiences. Michael Salmond uses practical and straightforward examples to clearly define and explore the key considerations of game and level designers alike. The content is diverse covering many topics, yet succinct and to the point. This book fills a critical void for video game education. * Johnny Luce, co-owner, software designer, and engineer at augzoo *This is an excellent book on level design, with a wealth of up-to-date and varied examples. It is highly visual and extremely readable, giving a comprehensive view of the area in a way that is colorful and engaging, whilst maintaining a good level of technicality. It is ideal for students studying game design, in order to develop their understanding of the theories and practices involved in level design as a specialism * J. Weinel, University of Greenwich, UK *Table of Contents1. What Is Level Design? 2. Creating Immersive, Believable Worlds 3. Design for Narrative 4. Environment Design vs Level Design 5. Building Worlds 6. Design for Single & Multiplayer 7. Level Design is Agile Design 8. The Language of Level Design 9. Prototyping Level Design 10. The Game Is the Level, the Level Is the Game 11. Communication and Final Touches 12. Where to Next?

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Book SynopsisExpert Guidance on the Math Needed for 3D Game ProgrammingDeveloped from the authors' popular Game Developers Conference (GDC) tutorial, Essential Mathematics for Games and Interactive Applications, Third Edition illustrates the importance of mathematics in 3D programming. It shows you how to properly animate, simulate, and render scenes and discusses the mathematics behind the processes.New to the Third EditionCompletely revised to fix errors and make the content flow better, this third edition reflects the increased use of shader graphics pipelines, such as in DirectX 11, OpenGL ES (GLES), and the OpenGL Core Profile. It also updates the material on real-time graphics with coverage of more realistic materials and lighting.The Foundation for Successful 3D ProgrammingThe book covers the low-level mathematical and geometric representations and algorithms that are the core of any game engine. It also explores all thTrade ReviewPraise for Previous Editions:"It’s the book with all the math you need for games."—Neil Kirby, Researcher, Alcatel-Lucent"Even though I’ve worked with these systems for years, this book showed me new ways of looking at several topics that make them easier to remember and use. For someone new to 3D programming, it is extremely useful—it gives them a solid background in pretty much every area they need to understand."—Peter Lipson, Toys for Bob, Inc.Table of ContentsRepresenting Real Numbers. Vectors and Points. Linear Transformations and Matrices. Affine Transformations. Orientation Representation. Interpolation. Viewing and Projection. Geometry and Programmable Shading. Lighting. Rasterization. Random Numbers. Intersection Testing. Rigid-Body Dynamics.

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Book SynopsisWinner of the 2017 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)A relatively new area of research, adversarial risk analysis (ARA) informs decision making when there are intelligent opponents and uncertain outcomes. Adversarial Risk Analysis develops methods for allocating defensive or offensive resources against intelligent adversaries. Many examples throughout illustrate the application of the ARA approach to a variety of games and strategic situations.Focuses on the recent subfield of decision analysis, ARA Compares ideas from decision theory and game theoryUses multi-agent influence diagrams (MAIDs) throughout to help readers visualize complex information structuresApplies the ARA approach to simultaneous games, auctions, sequential games, and defend-attack gamesContains an extended case study based on a real application in railway security, whichTrade Review"This well-written and concise text is an introduction to the field of adversarial risk analysis (ARA), which is a form of decision and risk analysis which incorporates uncertainty and game theory to model strategies of an adversary…There is an appropriate amount of detail throughout the book, making it suitable for a reference text as well as a book which may be read cover to cover and it is both thought provoking and enlightening."—Matthew Craven, Plymouth University, Journal of the Royal Statistical Society, Series A, January 2017 "Here, Banks (Duke Univ.), Rios (IBM), and Insua (ICMAT-CSIC, Spain) identify three categories of uncertainty for the strategist: aleatory uncertainty—nondeterminism of outcomes even after players make choices; epistemic uncertainty—hidden information concerning opponents' preferences, beliefs, and capabilities; and concept uncertainty—hidden information concerning opponents' strategies. Adversarial risk analysis, a new field with roots in modern efforts to defeat terrorism, provides a framework, in principle, to cope with these uncertainties. Solving the models seems generally intractable, but the heart of the book, the first of its kind, offers exemplary case studies. Summing up: Recommended. Lower-division undergraduates and above; informed general audiences."—D. V. Feldman, University of New Hampshire, Durham, USA, for CHOICE, March 2016 Table of ContentsGames and Decisions. Simultaneous Games. Auctions. Sequential Games. Variations on Sequential Defend-Attack Games. A Security Case Study. Other Issues. Solutions to Selected Exercises. References. Index.

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Book SynopsisThe newest addition to our Influential Video Game Designers series explores the work of Todd Howard, executive producer at Bethesda Studios, known for how he consistently pushes the boundaries of open-world gaming and player agency. Howard's games create worlds in which players can design their own characters and tell their own stories. While many games tell the story of the game's main character, Todd Howard's worldbuilding approach to game design focuses more on telling the story of the game's world, whether it be the high fantasy environments of the Elder Scrolls series or the post-apocalyptic wasteland of the Fallout series. This focus on sculpting the world allows for remarkable amounts of player freedom and choice in an expansive game environment by creating a landscape rich with open opportunity. Drawing on both academic discussions of narrative, world design, and game design, as well as on officially released interviews, speeches, and presentations given by HowardTrade ReviewIn Todd Howard: Worldbuilding in Tamriel and Beyond, Wendi Sierra illuminates this beloved game developer's mind, his struggles and passions, the history of his career from humble beginnings to towering success, and his visions for the future of games. Choosing to highlight his excellence in worldbuilding, she examines how rich, expansive game worlds like Tamriel keep players coming back again and again, logging hundreds or even thousands of in-game hours trudging up and down snowy mountains, collecting herbs, ore, and flowers, and questing for colorful NPCs—and for the sake of a compelling story in which they are the protagonist. This book is an essential guide to one of the greatest worldbuilders in the history of fantasy, and it belongs on the shelves of game scholars and game lovers alike. * Lauren Woolbright, Assistant Professor of Communication and New Media Studies, Alma College, USA *Table of Contents1: An Unlikely Beginning 2: Little Catastrophes 3: Set Pieces for Player Experience 4: Expanding the Game World 5: Todd Howard: In His Own Words 6: The Future of Open World Gaming Appendix - Chronology of Works Bibliography Index

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Book SynopsisTest your wits with the ultimate game of cunning, logic and intuition'This book is brilliant' Zoe Ball, BBC Radio 2*It's time to start your adventure. Get them before they get you*Put your sleuthing skills to the test in a world of deception, betrayal, and strategy. Placed in a castle in the Scottish Highlands, you must figure out if your fellow players are Faithful or a Traitor. Can you trust Jorge, the dentist with an encyclopaedic memory and tendency to smile at everyone? Or Nina, the retiree who acts like the group's matriarch but has a knowing glint in her eyes..? Beware, for in this treacherous game, trust is a luxury you cannot afford.In the official book of the BAFTA-winning phenomenon, The Traitors: The Interactive Game Book, the decisions you make will decide what happens next. Take this thrilling journey on your own or with others, pooling your wisdom to make the right choices. With over 20 standalone games to play in a group - all with cunning Traitors twists - this is the perfect gift, guaranteed to unleash hours of mischief and fun.*Praise for The Traitors TV show* 'Addictively fiendish, this treachery was the best thing on TV in 20 years' Daily Mail'By far and away the most compelling and engrossing reality show of 2022, if not all time' Rolling Stone'One of the hottest realities right now, The Traitors is an absolute phenomenon you can enjoy also in a book format. Now, this is not a normal book' Digital SpyTrade ReviewEver since the show aired, Traitors fans have been asking how they can be part of the wonderful world of the show . . . The book is full of all the mystery, suspense and fun of the show. * Amanda Lovett (Season 1 contestant, BBC The Traitors UK) *This book is brilliant * Zoe Ball, BBC Radio 2 *One of the hottest realities right now, The Traitors is an absolute phenomenon you can enjoy also in a book * Digital Spy *

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Book Synopsis

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