Game theory Books

Book SynopsisAn introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations.This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents “should” do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.Features:Each chapter begins with a motivating example that can

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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 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 SynopsisDesigned for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the mathematics classroom. From the Foreword No longer will you be just a spectator when people give you quantitative information—you will become an active participant who can engage and contribute new insights to any discussion.[…] There are many math books that will feed you knowledge, but it is rare to see a book like this one that will help you cultivate wisdom.[…] As the authors illustrate, mathematics that pays attention to human considerations can help you look at the world with a new lens, help you frame important questions, and help you make wise decisions. Francis Edward Su, Harvey Mudd CollegeTrade Review“This is a most revolutionary book, and I would love to teach a course using it! There is much interest in what is variously termed quantitative literacy (QL), quantitative reasoning (QR), and critical thinking (CT). This book is the first in a series of Texts for Quantitative Critical Thinking … . I do not want to fail to mention that the book’s layout is simply beautiful.” (Paul J. Campbell, Mathematics Magazine, Vol. 92 (1), November, 2018)Table of Contents1. Measuring.- 2. Flowing.- 3. Networking.- 4. Changing.- 5. Risking.- 6. Deciding.- 7. Case Studies.- 8. Resources.- List of Figures.- List of Tables.- Bibliography.- Index.

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Book SynopsisThis contributed volume focuses on aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. It covers theoretical developments, algorithmic methods, and applications to fields as varied as mathematical biology, environmental management, economics, engineering, guidance and control, and social interaction. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.Advances in Dynamic Games presents state-of-the-art research that serves as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 15th International Symposium of Dynamic Games and Applications held July 19–22, 2012, in Byšice, Czech Republic.Table of ContentsPart I Dynamic Games: Theory and Computation.- 1 Relative Value Iteration for Stochastic Differential Games.- 2 OPTGAME3: A Dynamic Game Solver and an Economic Example.- 3 Dynamic Programming Approach to Aircraft Control in a Windshear.- 4 Existence of Optimal Controls for a Bi-Level Optimal Control Problem.- 5 Static Linear-Quadratic Gaussian Games.- 6 Interior Convergence Under Payoff Monotone Selections and Proper Equilibrium: Application to Equilibrium Selection.- Part II Dynamic Games: Applications.- 7 Should a Retailer Support a Quality Improvements Strategy?.- 8 A Large Population Parental Care Game with Asynchronous Moves.- 9 Conditions for Cooperation and Trading in Value-Cost Dynamic Games.- 10 Intra-seasonal Strategies Based on Energy Budgets in a Dynamic Predator-Prey Game.- 11 On a Game-Theoretic Model of Environmental Pollution Problem.- Part III Pursuit-Evasion Games 12 Open-Loop Solvability Operator in Differential Games with Simple Motions in the Plane.- 13 Game with Two Pursuers and One Evader: Case of Weak Pursuers.- 14 Collaborative Interception of Moving Re-Locatable Target .- 15 The Effect of Pursuer Dynamics on the Value of Linear.- Pursuit-Evasion Games with Bounded Controls.

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Book SynopsisIn allen Arbeitsfeldern brauchen Ökonomen heute eine gute ökonomische Intuition gepaart mit mathematischem Sachverstand. Das Buch bietet eine kompakte und zugleich anspruchsvolle Einführung in die für Ökonomen wichtigsten Werkzeuge der Analysis, Optimierung und linearen Algebra. Dabei beschränken sich die Autoren nicht darauf, die verschiedenen Methoden, Regeln und Theoreme vorzustellen, vielmehr beweisen sie die wichtigsten Aussagen, um Lesern ein Verständnis für die Richtigkeit mathematischer Aussagen und Beweistechniken zu vermitteln.Trade ReviewAus den Rezensionen: "… Auf fast allen Arbeitsgebieten der Ökonomen ist eine gute mathematische Vorbildung äußerst hilfreich … Vor diesem Hintergrund … leitet der Bonner VWL-Professor Frank Riedel und sein wissenschaftlicher Mitarbeiter die wichtigsten Aussagen Schritt für Schritt her, so dass man als Leser den Zweck und die Zielgerichtetheit mathematischer Modelle und Beweistechniken begreift. Alle Methoden veranschaulichen die Autoren mit Praxisbeispielen … Nicht nur Studenten dürften von diesem Lehrbuch enorm profitieren. Auch Praktiker können aus den hier vermittelten Kenntnissen der höheren Mathematik Nutzen ziehen." (in: STUDIUM - Das Buchmagazin für Studierende, Wintersemester 2007/08, S. 16)Table of ContentsGrundlagen.- Mengen.- Zahlen.- Vollst#x00E4;ndige Induktion.- Analysis I.- Funktionen.- Folgen und Grenzwerte.- Stetigkeit.- Differentialrechnung.- Optimierung I.- Integration.- Lineare Algebra.- Vektorr#x00E4;ume.- Lineare Gleichungssysteme.- Weiterf#x00FC;hrende Themen.- Analysis II.- Topologie.- Differentialrechnung im #x2118;.- Optimierung II.- Weiterf#x00FC;hrende Themen.

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Book SynopsisDrawing on a diverse collection of institutional archives, personal correspondence and papers, and interviews, the author shows how game theory offered social scientists, biologists, military strategists, and others a common, flexible language that could facilitate wide-ranging thought and debate on some of the most critical issues of the day.Trade Review"Erickson has written a vital book. He shows how game theory has survived despite its repeated failure to fulfill the highest hopes of its exponents. This is an outstanding and sure-to-be influential study of twentieth-century science and social thought." (Joel Isaac, Christ's College, Cambridge)

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Book SynopsisDrawing on a diverse collection of institutional archives, personal correspondence and papers, and interviews, the author shows how game theory offered social scientists, biologists, military strategists, and others a common, flexible language that could facilitate wide-ranging thought and debate on some of the most critical issues of the day.Trade Review"Erickson has written a vital book. He shows how game theory has survived despite its repeated failure to fulfill the highest hopes of its exponents. This is an outstanding and sure-to-be influential study of twentieth-century science and social thought." (Joel Isaac, Christ's College, Cambridge)

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Book SynopsisIn this application of game theory to political phenomena, Cohen focuses on Chile and Brazil. He explores why democratic reforms failed in Latin America, arguing that political outcomes cannot be explained without treating beliefs and preferences as having a causal force in their own right.

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Book SynopsisEmpowers readers with the wisdom to win in every strategic situation.Trade Review"...a well-written account of wide-ranging real-world situations that show the nuts and bolts of game theory..." -- Engineering & Technology

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Book SynopsisPraise for the Second Edition: This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications. Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and tTable of ContentsPreface xi 1 Mathematical Models 1 1.1 Applying Mathematics 1 1.2 The Diet Problem 2 1.3 The Prisoner's Dilemma 5 1.4 The Roles of Linear Programming and Game Theory 8 2 The Linear Programming Model 9 2.1 History 9 2.2 The Blending Model 10 2.3 The Production Model 21 2.4 The Transportation Model 34 2.5 The Dynamic Planning Model 38 2.6 Summary 47 3 The Simplex Method 57 3.1 The General Problem 57 3.2 Linear Equations and Basic Feasible Solutions 63 3.3 Introduction to the Simplex Method 72 3.4 Theory of the Simplex Method 77 3.5 The Simplex Tableau and Examples 85 3.6 Artificial Variables 93 3.7 Redundant Systems 101 3.8 A Convergence Proof 106 3.9 Linear Programming and Convexity 110 3.10 Spreadsheet Solution of a Linear Programming Problem 115 4 Duality 121 4.1 Introduction to Duality 121 4.2 Definition of the Dual Problem 123 4.3 Examples and Interpretations 132 4.4 The Duality Theorem 138 4.5 The Complementary Slackness Theorem 154 5 Sensitivity Analysis 161 5.1 Examples in Sensitivity Analysis 161 5.2 Matrix Representation of the Simplex Algorithm 175 5.3 Changes in the Objective Function 183 5.4 Addition of a New Variable 189 5.5 Changes in the Constant-Term Column Vector 192 5.6 The Dual Simplex Algorithm 196 5.7 Addition of a Constraint 204 6 Integer Programming 211 6.1 Introduction to Integer Programming 211 6.2 Models with Integer Programming Formulations 214 6.3 Gomory's Cutting Plane Algorithm 228 6.4 A Branch and Bound Algorithm 237 6.5 Spreadsheet Solution of an Integer Programming Problem 244 7 The Transportation Problem 251 7.1 A Distribution Problem 251 7.2 The Transportation Problem 264 7.3 Applications 282 8 Other Topics in Linear Programming 299 8.1 An Example Involving Uncertainty 299 8.2 An Example with Multiple Goals 306 8.3 An Example Using Decomposition 314 8.4 An Example in Data Envelopment Analysis 325 9 Two-Person, Zero-Sum Games 337 9.1 Introduction to Game Theory 337 9.2 Some Principles of Decision Making in Game Theory 345 9.3 Saddle Points 350 9.4 Mixed Strategies 353 9.5 The Fundamental Theorem 360 9.6 Computational Techniques 370 9.7 Games People Play 382 10 Other Topics in Game Theory 391 10.1 Utility Theory 391 10.2 Two-Person, Non-Zero-Sum Games 393 10.3 Noncooperative Two-Person Games 397 10.4 Cooperative Two-Person Games 404 10.5 The Axioms of Nash 408 10.6 An Example 414 A Vectors and Matrices 417 B An Example of Cycling 421 C Efficiency of the Simplex Method 423 D LP Assistant 427 E Microsoft Excel and Solver 431 Bibliography 439 Solutions to Selected Problems 443 Index 457

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Book SynopsisGame-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk's Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito's stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical contextTable of ContentsPreface xi Acknowledgments xv Part I Examples in Discrete Time 1 1 Borel’s Law of Large Numbers 5 1.1 A Protocol for Testing Forecasts 6 1.2 A Game-Theoretic Generalization of Borel’s Theorem 8 1.3 Binary Outcomes 16 1.4 Slackenings and Supermartingales 18 1.5 Calibration 19 1.6 The Computation of Strategies 21 1.7 Exercises 21 1.8 Context 24 2 Bernoulli’s and De Moivre’s Theorems 31 2.1 Game-Theoretic Expected Value and Probability 33 2.2 Bernoulli’s Theorem for Bounded Forecasting 37 2.3 A Central Limit Theorem 39 2.4 Global Upper Expected Values for Bounded Forecasting 45 2.5 Exercises 46 2.6 Context 49 3 Some Basic Supermartingales 55 3.1 Kolmogorov’s Martingale 56 3.2 Doléans’s Supermartingale 56 3.3 Hoeffding’s Supermartingale 58 3.4 Bernstein’s Supermartingale 63 3.5 Exercises 66 3.6 Context 67 4 Kolmogorov’s Law of Large Numbers 69 4.1 Stating Kolmogorov’s Law 70 4.2 Supermartingale Convergence Theorem 73 4.3 How Skeptic Forces Convergence 80 4.4 How Reality Forces Divergence 81 4.5 Forcing Games 82 4.6 Exercises 86 4.7 Context 89 5 The Law of the Iterated Logarithm 93 5.1 Validity of the Iterated-Logarithm Bound 94 5.2 Sharpness of the Iterated-Logarithm Bound 99 5.3 Additional Recent Game-Theoretic Results 100 5.4 Connections with Large Deviation Inequalities 104 5.5 Exercises 104 5.6 Context 106 Part II Abstract Theory in Discrete Time 109 6 Betting on a Single Outcome 111 6.1 Upper and Lower Expectations 113 6.2 Upper and Lower Probabilities 115 6.3 Upper Expectations with Smaller Domains 118 6.4 Offers 121 6.5 Dropping the Continuity Axiom 125 6.6 Exercises 127 6.7 Context 131 7 Abstract Testing Protocols 135 7.1 Terminology and Notation 136 7.2 Supermartingales 136 7.3 Global Upper Expected Values 142 7.4 Lindeberg’s Central Limit Theorem for Martingales 145 7.5 General Abstract Testing Protocols 146 7.6 Making the Results of Part I Abstract 151 7.7 Exercises 153 7.8 Context 155 8 Zero-One Laws 157 8.1 Lévy’s Zero-One Law 158 8.2 Global Upper Expectation 160 8.3 Global Upper and Lower Probabilities 162 8.4 Global Expected Values and Probabilities 163 8.5 Other Zero-One Laws 165 8.6 Exercises 169 8.7 Context 170 9 Relation to Measure-Theoretic Probability 175 9.1 Ville’s Theorem 176 9.2 Measure-Theoretic Representation of Upper Expectations 180 9.3 Embedding Game-Theoretic Martingales in Probability Spaces 189 9.4 Exercises 191 9.5 Context 192 Part III Applications in Discrete Time 195 10 Using Testing Protocols in Science and Technology 197 10.1 Signals in Open Protocols 198 10.2 Cournot’s Principle 201 10.3 Daltonism 202 10.4 Least Squares 207 10.5 Parametric Statistics with Signals 212 10.6 Quantum Mechanics 215 10.7 Jeffreys’s Law 217 10.8 Exercises 225 10.9 Context 226 11 Calibrating Lookbacks and p-Values 229 11.1 Lookback Calibrators 230 11.2 Lookback Protocols 235 11.3 Lookback Compromises 241 11.4 Lookbacks in Financial Markets 242 11.5 Calibrating p-Values 245 11.6 Exercises 248 11.7 Context 250 12 Defensive Forecasting 253 12.1 Defeating Strategies for Skeptic 255 12.2 Calibrated Forecasts 259 12.3 Proving the Calibration Theorems 264 12.4 Using Calibrated Forecasts for Decision Making 270 12.5 Proving the Decision Theorems 274 12.6 From Theory to Algorithm 286 12.7 Discontinuous Strategies for Skeptic 291 12.8 Exercises 295 12.9 Context 299 Part IV Game-Theoretic Finance 305 13 Emergence of Randomness in Idealized Financial Markets 309 13.1 Capital Processes and Instant Enforcement 310 13.2 Emergence of Brownian Randomness 312 13.3 Emergence of Brownian Expectation 320 13.4 Applications of Dubins–Schwarz 325 13.5 Getting Rich Quick with the Axiom of Choice 331 13.6 Exercises 333 13.7 Context 334 14 A Game-Theoretic Itô Calculus 339 14.1 Martingale Spaces 340 14.2 Conservatism of Continuous Martingales 348 14.3 Itô Integration 350 14.4 Covariation and Quadratic Variation 355 14.5 Itô’s Formula 357 14.6 Doléans Exponential and Logarithm 358 14.7 Game-Theoretic Expectation and Probability 360 14.8 Game-Theoretic Dubins–Schwarz Theorem 361 14.9 Coherence 362 14.10 Exercises 363 14.11 Context 365 15 Numeraires in Market Spaces 371 15.1 Market Spaces 372 15.2 Martingale Theory in Market Spaces 375 15.3 Girsanov’s Theorem 376 15.4 Exercises 382 15.5 Context 382 16 Equity Premium and CAPM 385 16.1 Three Fundamental Continuous I-Martingales 387 16.2 Equity Premium 389 16.3 Capital Asset Pricing Model 391 16.4 Theoretical Performance Deficit 395 16.5 Sharpe Ratio 396 16.6 Exercises 397 16.7 Context 398 17 Game-Theoretic Portfolio Theory 403 17.1 Stroock–Varadhan Martingales 405 17.2 Boosting Stroock–Varadhan Martingales 407 17.3 Outperforming the Market with Dubins–Schwarz 413 17.4 Jeffreys’s Law in Finance 414 17.5 Exercises 415 17.6 Context 416 Terminology and Notation 419 List of Symbols 425 References 429 Index 455

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Book SynopsisThe first practical trading guide to the revolutionary new science of decision-making According to the Wall Street Journal, Game theory is hot. On Wall Street, many of today''s most successful high-rollers now use it to help them make crucial buying and selling decisions. In the first trader''s guide to game theory, economist Ron Shelton uses real-world case studies to demonstrate how game theory works in trading. He provides a model that can be used to predict the profitability of trades and shows traders how to use it to make market buy and sell decisions.Trade Review"...a worthwhile read..."Interactive Investor, Tuesday 17 June 2008Table of ContentsWhat is Game Theory? Basic Ideas About Financial Markets. The Interaction Between Price Fluctuations and Risk AcceptanceLevels. Constructing a Game Theoretic Model. Understanding the Model. Treasury Bond Futures. Appendices. Index.

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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 SynopsisWhen John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive. This book presents Nash's contributions not only to game theory, for which he received the Nobel, but to mathematics - from Riemannian geometry and partial differential equations - in which he commands greater acclaim among academics.Trade Review"If you want to see a sugary Hollywood depiction of John Nash's life, go to the cinema. Afterwards, if you are curious about his insights, pick up a new book that explains his work and reprints his most famous papers. It is just as amazing as his personal story."--Chris Giles, Financial Times "One of the most beautifully designed economics books I have ever seen and at a low price... Why are we so intrigued by the story of John Nash? We are curious to understand a person who proves theorems we are unable to fathom. We imagine the voices from another world he has heard. We ask where he was for 30 years during which he walked among us but wasn't here. We are frightened and we are attracted by this combination of 'crazy' and 'genius', an invitation for visiting the edge of our own minds."--Ariel Rubinstein, The Times Higher Education Supplement "Any mathematician who read A Beautiful Mind ... had to be looking for the appendices--the ones explaining what Nash actually did to earn his formidable reputation within the mathematical community. Well, here they are, in a beautifully produced volume... Kuhn, Nasar, and the other contributors have performed a most welcome service by collaborating to bring together the pieces missing from A Beautiful Mind... The mathematical community is eternally in their debt."--SIAM News "The book is written in a pleasant and informal style, addressed to a large audience."--P.T. Moranu, MathematicaTable of ContentsPREFACE by Harold W. Kuhn vii INTRODUCTION by Sylvia Nasar xi Chapter 1: Press Release--The Royal Swedish Academy of Sciences 1 Chapter 2: Autobiography 5 Photo Essay 13 Editor's introduction to Chapter 3 29 Chapter 3: The Game of Hex by John Milnor 31 Editor's Introduction to Chapter 4 35 Chapter 4: The bargaining problem 37 Editor's Introduction to Chapters 5, 6, and 7 47 Chapter 5: Equilibrium Points in n-Person games 49 Chapter 6: Non-Cooperative Games Facsimile of Ph.D. Thesis 51 Chapter 7: Non-Cooperative Games 85 Chapter 8: Two-Person Coooperative Games 99 Editor's Introduction to Chapter 9 115 Chapter 9: Parallel Control 117 Chapter 10: real Algebraic Manifolds 127 Chapter 11: The Imbedding problem for Riemannian Manifolds 151 Chapter 12: Continuity of Solutions of Parabolic and Elliptic Equations 211 AFTERWORD 241 SOURCES 243

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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 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 SynopsisWe all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory. This book gives us the complete history of this area of mathematics, from its classical analytical beginnings to the present day.Trade Review"In the 18th century, mathematicians began to tease apart how best to track down and intercept prey, inspired by pirate ships bearing down on merchant vessels. The mathematics is by no means trivial, and quickly becomes fiendish if the merchant ship takes evasive action. This is just one of the colorful problems in Paul Nahin's fascinating history of the mathematics of pursuit, in which he guides us masterfully through the maths itself--think lions and Christians, submarines and torpedoes, and the curvaceous flight of fighter aircraft."--New Scientist "This is a highly readable book that offers several colorful applications of differential equations and good examples of non-trivial integrals for calculus students. It would be a good source of examples for the classroom and or a starting point for an independent project."--Bill Satzer, MAA Review "This book contains a well-written, well-organized collection of solutions to twenty-one challenging calculus and differential equation problems that concern pursuit and evasion as well as the historical background of each problem type."--Mathematics Teacher "I am sure that this book will appeal to everyone who is interested in mathematics and game theory. Excellent work."--Prabhat Kumar Mahanti, Zentralblatt Math "Chases and Escapes is a wonderful collection of interesting and classic pursuit and evasion problems... If you are interested in in dogs chasing ducks, pirates chasing merchants, and submarines hiding, then this book is for you."--Mathematics TeacherTable of ContentsPreface to the Paperback Edition xiii What You Need to Know to Read This Book (and How I Learned What I Needed to Know to Write It) xxvii Introduction 1 Chapter 1. The Classic Pursuit Problem 7 *1.1 Pierre Bouguer's Pirate Ship Analysis 7 *1.2 A Modern Twist on Bouguer 17 *1.3 Before Bouguer: The Tractrix 23 *1.4 The Myth of Leonardo da Vinci 27 *1.5 Apollonius Pursuit and Ramchundra's Intercept Problem 29 Chapter 2. Pursuit of (Mostly) Maneuvering Targets 41 *2.1 Hathaway's Dog-and-Duck Circular Pursuit Problem 41 *2.2 Computer Solution of Hathaway's Pursuit Problem 52 *2.3 Velocity and Acceleration Calculations for a Moving Body 64 *2.4 Houghton's Problem: A Circular Pursuit That Is Solvable in Closed Form 78 *2.5 Pursuit of Invisible Targets 85 *2.6 Proportional Navigation 93 Chapter 3. Cyclic Pursuit 106 *3.1 A Brief History of the n-Bug Problem, and Why It Is of Practical Interest 106 *3.2 The Symmetrical n-Bug Problem 110 *3.3 Morley's Nonsymmetrical 3-Bug Problem 116 Chapter 4. Seven Classic Evasion Problems 128 *4.1 The Lady-in-the-Lake Problem 128 *4.2 Isaacs's Guarding-the-Target Problem 138 *4.3 The Hiding Path Problem 143 *4.4 The Hidden Object Problem: Pursuit and Evasion as a Simple Two-Person, Zero-Sum Game of Attack-and-Defend 156 *4.5 The Discrete Search Game for a Stationary Evader -- Hunting for Hiding Submarines 168 *4.6 A Discrete Search Game with a Mobile Evader -- Isaacs's Princess-and-Monster Problem 174 *4.7 Rado's Lion-and-Man Problem and Besicovitch's Astonishing Solution 181 Appendix A Solution to the Challenge Problems of Section 1.1 187 Appendix B Solutions to the Challenge Problems of Section 1.2 190 Appendix C Solution to the Challenge Problem of Section 1.5 198 Appendix D Solution to the Challenge Problem of Section 2.2 202 Appendix E Solution to the Challenge Problem of Section 2.3 209 Appendix F Solution to the Challenge Problem of Section 2.5 214 Appendix G Solution to the Challenge Problem of Section 3.2 217 Appendix H Solution to the Challenge Problem of Section 4.3 219 Appendix I Solution to the Challenge Problem of Section 4.4 222 Appendix J Solution to the Challenge Problem of Section 4.7 224 Appendix K Guelman's Proof 229 Notes 235 Bibliography 245 Acknowledgments 249 Index 251

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Book SynopsisGame theory--the study of how people make choices while interacting with others--is one of the most popular technical approaches in social science today. But as Michael Chwe reveals in his insightful new book, Jane Austen explored game theory's core ideas in her six novels roughly two hundred years ago. Jane Austen, Game Theorist shows how this belTrade Review"Jane Austen, Game Theorist ... is more than the larky scholarly equivalent of 'Pride and Prejudice and Zombies.'... Mr. Chwe argues that Austen isn't merely fodder for game-theoretical analysis, but an unacknowledged founder of the discipline itself: a kind of Empire-waisted version of the mathematician and cold war thinker John von Neumann, ruthlessly breaking down the stratagems of 18th-century social warfare."--Jennifer Schuessler, New York Times "[A] convincing case for how mathematical models and fictional narratives can work towards reciprocal illustration."--Jonathan Sachs, Times Literary Supplement "This is insightful literary analysis at its most accessible and enjoyable."--Kate Hutchings, Huffington Post Books "Jane Austen, Game Theorist should join the list of strategic classics like The Art of War ... on the shelf of everybody who wants to be effective in life."--Diane Coyle, Enlightenment Economics "Chwe makes an argument for Austen as a founder of decision science in this 2013 book that boasts an impressive array of diagrams and hard-nosed textual analysis."--Evelyn Crowley, Vogue.com "This is such a fabulous book--carefully written, thoughtful and insightful."--Guardian.co.uk's Grrl Scientist blog "[B]lends two very different subjects--game theory and literature--delightfully."--Siddarth Singh, Mint "Well researched and with an excellent index, the book will appeal to Austen fans who can see her characters in another light."--Choice "When an intelligent, knowledgeable reader with a new distinctive viewpoint engages intensely with a great work of literature, the results are usually worthy of attention. There is much that is valuable in Chwe's book."--Ernest Davis, SIAM NewsTable of ContentsPreface xi Abbreviations xiii CHAPTER ONE The Argument 1 CHAPTER TWO Game Theory in Context 9 * Rational Choice Theory 9 * Game Theory 12 * Strategic Thinking 15 * How Game Theory Is Useful 19 * Criticisms 25 * Game Theory and Literature 30 CHAPTER THREE Folktales and Civil Rights 35 CHAPTER FOUR Flossie and the Fox 43 CHAPTER FIVE Jane Austen's Six Novels 49 *Pride and Prejudice 50 *Sense and Sensibility 54 *Persuasion 60 *Northanger Abbey 67 *Mansfield Park 75 *Emma 86 CHAPTER SIX Austen's Foundations of Game Theory 97 * Choice 97 * Preferences 102 * Revealed Preferences 105 * Names for Strategic Thinking 107 * Strategic Sophomores 111 * Eyes 113 CHAPTER SEVEN Austen's Competing Models 115 * Emotions 115 * Instincts 119 * Habits 121 * Rules 124 * Social Factors 127 * Ideology 128 * Intoxication 130 * Constraints 130 CHAPTER EIGHT Austen on What Strategic Thinking Is Not 133 * Strategic Thinking Is Not Selfish 133 * Strategic Thinking Is Not Moralistic 134 * Strategic Thinking Is Not Economistic 135 * Strategic Thinking Is Not About Winning Inconsequential Games 137 CHAPTER NINE Austen's Innovations 141 * Partners in Strategic Manipulation 141 * Strategizing About Yourself 153 * Preference Change 158 * Constancy 167 CHAPTER TEN Austen on Strategic Thinking's Disadvantages 171 CHAPTER ELEVEN Austen's Intentions 179 CHAPTER TWELVE Austen on Cluelessness 188 * Lack of Natural Ability 188 * Social Distance 198 * Excessive Self-Reference 200 * High-Status People Are Not Supposed to Enter the Minds of Low-Status People 202 * Presumption Sometimes Works 205 * Decisive Blunders 205 CHAPTER THIRTEEN Real-World Cluelessness 211 * Cluelessness Is Easier 211 * Difficulty Embodying Low-Status Others 213 * Investing in Social Status 217 * Improving Your Bargaining Position 219 * Empathy Prevention 224 * Calling People Animals 225 CHAPTER FOURTEEN Concluding Remarks 228 References 235 Index 251

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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 SynopsisPrice theory is a powerful analytical toolkit for measuring, explaining, and predicting human behavior in the marketplace. This incisive textbook provides an essential introduction to the subject, offering a diverse array of practical methods that empower students to learn by doing.Trade Review"A tremendous resource. This comprehensive and innovative book brings together in one great package the Chicago way of thinking about price theory."—Douglas A. Irwin, author of Free Trade under Fire

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Book Synopsis

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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 SynopsisIn this path-breaking theoretical work, political scientist Steven Brams and mathematician Mark Kilgour show how game theory can be applied to the rigorous development and thoughtful analysis of several critical problems that afflict the security of nations, from the deterrence of foes who might launch attacks, to the stabilization of crises that could explode into wars. In addition, they analyze a variety of related questions, including the interlocking preferences that fuel arms races, the strategic impact that Star Wars may have on nuclear deterrence, and optimal strategies for verifying arms control treaties. Of interest to students on international relations and foreign policy as well as those concerned with the formal analysis of conflict, Game Theory and National Security provides new foundations for understanding the rational basis of international conflict.Table of ContentsI. Introduction II. Arms Races III. Deterrence IV. Winding Down V. Star Wars VI. Optimal Threats VII. Crisis Instability VIII. Verification IX. National Security and War.

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Book SynopsisThe mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. ""Change,"" for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely used, a general mathematical assessment of potential pitfalls is missing. These realities provide opportunities to create new mathematical approaches.These themes are described in an introductory, expository, and accessible manner by exploring new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognize unexpected modeling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting (where the ""wrong"" person could win), nonparametric statistical, and economic ""supply and demand"" properties.Table of Contents Preface Chapter 1: Evolutionary game theory Chapter 2: All those puzzling voting mysteries! Chapter 3: Voting theory applied elsewhere Chapter 4: Voting: Symmetry and decompositions Chapter 5: Game theory: A decomposition Chapter 6: The reductionist approach Bibliography Index

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Book SynopsisKey environmental issues, such as biodiversity and climate change, have in recent years become more pressing than ever. Where the critical papers in the early 1990s explained the difficulties of cooperation in tackling transboundary environmental problems, later works have analyzed the various alternatives, and increased our understanding of various institutional designs and negotiation protocols’ impact on the success of cooperation. This collection brings together the most important articles on the game theoretic analysis of international environmental cooperation to both confront the cooperative and non-cooperative approaches to this, and demonstrate the diversity of methods used to analyze international environmental agreements.Trade Review'As the nations of the world struggle to negotiate an effective post-Kyoto international climate agreement, there is no area of economic scholarship that has more to offer than game theory. Michael Finus and Alejandro Caparrós, themselves leading scholars in this realm, have assembled a dream team of authors and a remarkable set of key articles from the best economics journals to produce a book with close to 50 chapters that should be essential reading for novices as well as experienced researchers' -- Robert Stavins, John F. Kennedy School of Government, Harvard University, USTable of ContentsContents: Acknowledgements Introduction Michael Finus and Alejandro Caparrós PART I FOUNDATIONS 1. Karl-Göran Mäler (1989), ‘The Acid Rain Game’, in H. Folmer and E. van Ierland (eds), Valuation Methods and Policy Making in Environmental Economics, Chapter 12, Amsterdam, The Netherlands: Elsevier, 231–52 2. Scott Barrett (1994), ‘Self-Enforcing International Environmental Agreements’, Oxford Economic Papers, Special Issue on Environmental Economics, 46, October, 878–94 3. Carlo Carraro and Domenico Siniscalco (1993), ‘Strategies for the International Protection of the Environment’, Journal of Public Economics, 52 (3), October, 309–28 4. Michael Hoel (1992), ‘International Environment Conventions: The Case of Uniform Reductions of Emissions’, Environmental and Resource Economics, 2 (2), March, 141–59 5. Parkash Chander and Henry Tulkens (1997), ‘The Core of an Economy with Multilateral Environmental Externalities’, International Journal of Game Theory, 26 (3), October, 379–401 PART II TECHNICAL ADVANCES 6. Effrosyni Diamantoudi and Eftichios S. Sartzetakis (2006), ‘Stable International Environmental Agreements: An Analytical Approach’, Journal of Public Economic Theory, 8 (2), May, 247–63 7. Santiago J. Rubio and Alistair Ulph (2006), ‘Self-Enforcing International Environmental Agreements Revisited’, Oxford Economic Papers, 58 (2), April, 233–63 8. Larry Karp and Leo Simon (2013), ‘Participation Games and International Environmental Agreements: A Non-Parametric Model’, Journal of Environmental Economics and Management, 65 (2), March, 326–44 9. Carsten Helm (2001), ‘On the Existence of a Cooperative Solution for a Coalitional Game with Externalities’, International Journal of Game Theory, 30 (1), September, 141–6 PART III COMPLIANCE 10. Rögnvaldur Hannesson (1997), ‘Fishing as a Supergame’, Journal of Environmental Economics and Management, 32 (3), March, 309–22 11. Michael Finus and Sigve Tjøtta (2003), ‘The Oslo Protocol on Sulfur Reduction: The Great Leap Forward?’ Journal of Public Economics, 87 (9–10), September, 2031–48 12. Henk Folmer, Pierre v. Mouche and Shannon Ragland (1993), ‘Interconnected Games and International Environmental Problems’, Environmental and Resource Economics, 3 (4), August, 313–35 13. Anke Gerber and Philipp C. Wichardt (2009), ‘Providing Public Goods in the Absence of Strong Institutions’, Journal of Public Economics, 93 (3–4), April, 429–39 14. Todd L. Cherry and David M. McEvoy (2013), ‘Enforcing Compliance with Environmental Agreements in the Absence of Strong Institutions: An Experimental Analysis’, Environmental and Resource Economics, 54 (1), January, 63–77 15. David M. McEvoy and John K. Stranlund (2009), ‘Self-Enforcing International Environmental Agreements with Costly Monitoring for Compliance’, Environmental and Resource Economics, 42 (4), April, 491–508 16. Nori Tarui, Charles F. Mason, Stephen Polasky and Greg Ellis (2008), ‘Cooperation in the Commons with Unobservable Actions’, Journal of Environmental Economics and Management, 55 (1), January, 37–51 17. Prajit K. Dutta and Roy Radner (2009) ‘A Strategic Analysis of Global Warming: Theory and Some Numbers’, Journal of Economic Behavior and Organization, 71 (2), August, 187–209 PART IV NEGOTIATIONS, SECOND-BEST DESIGNS AND INSTITUTIONS 18. Michael Finus and Bianca Rundshagen (1998), ‘Toward a Positive Theory of Coalition Formation and Endogenous Instrumental Choice in Global Pollution Control’, Public Choice, 96 (1–2), July, 145–86 19. Scott Barrett (2002), ‘Consensus Treaties’, Journal of Institutional and Theoretical Economics, 158 (4), December, 529–47 20. Pierre Courtois and Guillaume Haeringer (2012), ‘Environmental Cooperation: Ratifying Second-Best Agreements’, Public Choice, 151 (3–4), June, 565–84 21. A. Caparrós, J.-C. Péreau and T. Tazdaït (2004), ‘North-South Climate Change Negotiations: A Sequential Game with Asymmetric Information’, Public Choice, 121 (3–4), December, 455–80 22. Alejandro Caparrós and Jean-Christophe Péreau (2013), ‘Forming Coalitions to Negotiate North–South Climate Agreements’, Environment and Development Economics, Special Issue on Strategic Behaviour and Environmental Commons, 18 (1), February, 69–92 23. Bård Harstad (2012), ‘Climate Contracts: A Game of Emissions, Investments, Negotiations, and Renegotiations’, Review of Economic Studies, 79 (4), October, 1527–57 24. Carlo Carraro, Carmen Marchiori and Sonia Oreffice (2009), ‘Endogenous Minimum Participation in International Environmental Treaties’, Environmental and Resource Economics, 42 (3), March, 411–25 25. Astrid Dannenberg, Andreas Lange and Bodo Sturm (2014), ‘Participation and Commitment in Voluntary Coalitions to Provide Public Goods’, Economica, 81 (322), April, 257–75 26. Scott Barrett (2006), ‘Climate Treaties and “Breakthrough” Technologies’, American Economic Review, 96 (2), May, 22–5 27. Michael Hoel and Aart de Zeeuw (2010), ‘Can a Focus on Breakthrough Technologies Improve the Performance of International Environmental Agreements?’, Environmental and Resource Economics, 47 (3), November, 395–406 PART V TRANSFERS, SHARING AND FAIRNESS 28. Matthew McGinty (2007), ‘International Environmental Agreements among Asymmetric Nations’, Oxford Economic Papers, 59 (1), January, 45–62 29. Hans-Peter Weikard (2009), ‘Cartel Stability Under An Optimal Sharing Rule’, Manchester School, 77 (5), September, 575–93 30. Carlo Carraro, Johan Eyckmans and Michael Finus (2006), ‘Optimal Transfers and Participation Decisions in International Environmental Agreements’, Review of International Organizations, 1 (4), December, 379–96 31. Matthew McGinty, Garrett Milam and Alejandro Gelves (2012), ‘Coalition Stability in Public Goods Provision: Testing an Optimal Allocation Rule’, Environmental and Resource Economics, 52 (3), July, 327–45 32. Stefan Ambec and Yves Sprumont (2002), ‘Sharing a River’, Journal of Economic Theory, 107 (2), December, 453–62 33. Andreas Lange and Carsten Vogt (2003), ‘Cooperation in International Environmental Negotiations due to a Preference for Equity’, Journal of Public Economics, 87 (9–10), September, 2049–67 34. Michael Kosfeld, Akira Okada and Arno Riedl (2009), ‘Institution Formation in Public Goods Games’, American Economic Review, 99 (4), September, 1335–55 PART VI MULTIPLE COALITIONS 35. Francesco Bosello, Barabara Buchner and Carlo Carraro (2003), ‘Equity, Development, and Climate Change Control’, Journal of the European Economic Association, 1 (2–3), April–May, 601–11 36. Johan Eyckmans and Michael Finus (2006), ‘Coalition Formation in a Global Warming Game: How the Design of Protocols Affects the Success of Environmental Treaty-Making’, Natural Resource Modeling, 19 (3), September, 323–58 37. Geir B. Asheim, Camilla Bretteville Froyn, Jon Hovi and Fredric C. Menz (2006), ‘Regional versus Global Cooperation for Climate Control’, Journal of Environmental Economics and Management, 51 (1), January, 93–109 PART VII UNCERTAINTY, RISK AND CATASTROPHIC EVENTS 38. Seong-lin Na and Hyun Song Shin (1998), ‘International Environmental Agreements under Uncertainty’, Oxford Economic Papers, 50 (2), April, 173–85 39. Michael Finus and Pedro Pintassilgo (2013), ‘The Role of Uncertainty and Learning for the Success of International Climate Agreements’, Journal of Public Economics, 103, July, 29–43 40. Alfred Endres and Cornelia Ohl (2001), ‘International Environmental Cooperation in the One Shot Prisoners' Dilemma’, Schmollers Jahrbuch, Zeitschrift für Wirtschafts- und Sozialwissenschaften/Journal of Applied Social Science Studies, 121 (1), 1–26 41. Vincent Boucher and Yann Bramoullé (2010), ‘Providing Global Public Goods under Uncertainty’, Journal of Public Economics, 94 (9–10), October, 591–603 42. Scott Barrett (2013), ‘Climate Treaties and Approaching Catastrophes’, Journal of Environmental Economics and Management, 66 (2), September, 235–50 43. Alessandro Tavoni, Astrid Dannenberg, Giorgos Kallis and Andreas Löschel (2011), ‘Inequality, Communication, and The Avoidance of Disastrous Climate Change in a Public Goods Game’, Proceedings of the National Academy of Sciences, 108 (29), July, 11825–9 44. Lata Gangadharan and Veronika Nemes (2009) ‘Experimental Analysis of Risk and Uncertainty in Provisioning Private and Public Goods’, Economic Inquiry 47 (1), January, 146–64 PART VIII DYNAMIC COALITION FORMATION 45. Santiago J. Rubio and Alistair Ulph (2007), ‘An Infinite-Horizon Model of Dynamic Membership of International Environmental Agreements’, Journal of Environmental Economics and Management, 54 (3), November, 296–310 46. Aart de Zeeuw (2008), ‘Dynamic Effects on the Stability of International Environmental Agreements’, Journal of Environmental Economics and Management, 55 (2), March, 163–74 47. Marc Germain, Philippe Toint, Henry Tulkens and Aart de Zeeuw (2003), ‘Transfers to Sustain Dynamic Core-Theoretic Cooperation in International Stock Pollutant Control’, Journal of Economic Dynamics and Control, 28 (1), October, 79–99 48. Hans-Peter Weikard, Rob Dellink and Ekko van Ierland (2010), ‘Renegotiations in the Greenhouse’, Environmental and Resource Economics, 45 (4), April, 573–96 49. Michèle Breton, Lucia Sbragia and Georges Zaccour (2010), ‘A Dynamic Model for International Environmental Agreements’, Environmental and Resource Economics, 45 (1), January, 25–48 Index

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Book SynopsisBuilding on the success of the first edition, Game Theory and Public Policy, Second Edition provides a critical, selective review of key concepts in game theory with a view to their applications in public policy. The author further suggests modifications for some of the models (chiefly in cooperative game theory) to improve their applicability to economics and public policy.Roger McCain makes use of the analytical tools of game theory for the pragmatic purpose of identifying problems and exploring potential solutions, providing a toolkit for the analysis of public policy allowing for a clearer understanding of the public policy enterprise itself. His critical review of major topics from both cooperative and non-cooperative game theory includes less-known ideas and constructive proposals for new approaches. This revised edition features a new second half that focuses on biform games, combining cooperative and non-cooperative decisions in a simple and natural way to provide a working model of externalities that can be applied to issues such as monopoly policy and labor market policies.Drawing on comparatively well understood models in cooperative game theory and the author's own research on mathematical models of biform games, this unique approach and treatment of game theory, updated and expanded to stay on the cutting edge, will be a useful resource for students and scholars of economics and public policy, as well as for policymakers themselves.Trade ReviewAcclaim for the first edition:'[T]he McCain book is a thoughtful and thought-provoking survey of the post-war game theoretic literature. It is notable for its clear exposition, its willingness to acknowledge weaknesses and ambiguities of game theory, and its many illustrations. It would make an excellent text for students who have already learned a bit of game theory in earlier classes and who are open to broader issues than those covered in more mathematical and more elementary books. It is also good bedtime reading for academics who use a bit of game theory in their own work and for theorists who are interested in methodological issues associated with rational choice models.' --Roger D. Congleton, Public AdministrationTable of ContentsContents: Preface PART I HISTORICAL AND CRITICAL SURVEY 1. Objectives and scope of the book 2. Representing games 3. A brief interpretive history of game theory 4. Nash equilibrium and public policy 5. Correlated equilibrium 6. Noncooperative games in extensive form and public policy 7. Social mechanism design 8. Superadditive games in coalition function form 9. Recall, rationality and political economy PART II MIXED COOPERATIVE AND NONCOOPERATIVE DECISIONS: EXTENSIONS 10. Biform games and considerable solutions 11. The firm as a coalition 12. What coalitions will be formed? 13. Monopoly and monopsony revisited 14. Bargaining and the determination of wages 15. Bargaining power and majority rule References Index

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Book SynopsisBuilding on the success of the first edition, Game Theory and Public Policy, Second Edition provides a critical, selective review of key concepts in game theory with a view to their applications in public policy. The author further suggests modifications for some of the models (chiefly in cooperative game theory) to improve their applicability to economics and public policy.Roger McCain makes use of the analytical tools of game theory for the pragmatic purpose of identifying problems and exploring potential solutions, providing a toolkit for the analysis of public policy allowing for a clearer understanding of the public policy enterprise itself. His critical review of major topics from both cooperative and non-cooperative game theory includes less-known ideas and constructive proposals for new approaches. This revised edition features a new second half that focuses on biform games, combining cooperative and non-cooperative decisions in a simple and natural way to provide a working model of externalities that can be applied to issues such as monopoly policy and labor market policies.Drawing on comparatively well understood models in cooperative game theory and the author's own research on mathematical models of biform games, this unique approach and treatment of game theory, updated and expanded to stay on the cutting edge, will be a useful resource for students and scholars of economics and public policy, as well as for policymakers themselves.Trade ReviewAcclaim for the first edition:'[T]he McCain book is a thoughtful and thought-provoking survey of the post-war game theoretic literature. It is notable for its clear exposition, its willingness to acknowledge weaknesses and ambiguities of game theory, and its many illustrations. It would make an excellent text for students who have already learned a bit of game theory in earlier classes and who are open to broader issues than those covered in more mathematical and more elementary books. It is also good bedtime reading for academics who use a bit of game theory in their own work and for theorists who are interested in methodological issues associated with rational choice models.' --Roger D. Congleton, Public AdministrationTable of ContentsContents: Preface PART I HISTORICAL AND CRITICAL SURVEY 1. Objectives and scope of the book 2. Representing games 3. A brief interpretive history of game theory 4. Nash equilibrium and public policy 5. Correlated equilibrium 6. Noncooperative games in extensive form and public policy 7. Social mechanism design 8. Superadditive games in coalition function form 9. Recall, rationality and political economy PART II MIXED COOPERATIVE AND NONCOOPERATIVE DECISIONS: EXTENSIONS 10. Biform games and considerable solutions 11. The firm as a coalition 12. What coalitions will be formed? 13. Monopoly and monopsony revisited 14. Bargaining and the determination of wages 15. Bargaining power and majority rule References Index

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Book SynopsisEconomic theory and philosophy have discussed concepts of fairness, but the criteria of fairness are in each case absolute: a situation is either fair or it is not. This book draws on these literatures to propose two criteria of relative fairness, and a hierarchical rule for the priority of application of these criteria, with a view to comparison of practicable alternatives in public policy. A veil-of-ignorance device of representation of rational fairness is used to argue that these criteria are normatively relevant. Applications to intergenerational fairness, fairness among regions in the context of migration, externalities and Pigovian taxes, to fair prices and wages, and to relative fairness in the status of racial and caste groups are sketched. The book is designed with real world public policy practice.Scholars with an interest in the economic evaluation of public policy will find this compelling book essential reading.Trade Review'Roger McCain's new book develops an original analysis of relative fairness or ''quasifairness'' to compare stable social situations as objects of public policy. Employing bounded rationality, Rawls, and a game-theoretic understanding of social stability, the book's applications are far-reaching and penetrating. Strongly recommended as a new strategy for re-grounding normative economics.' -- John B. Davis, Marquette University, US and University of Amsterdam, the NetherlandsTable of ContentsContents: 1. Fairness in a system of cooperative, joint production 2. Decision, cooperation and stability 3. Side payments in effectivity analysis of cooperative games 4. Efficiency and fairness 5. The veil of ignorance 6. Intergenerational transfers 7. Intergenerational transfers: some complications 8. Interregional fairness, migration and efficiency 9. Policy, externality, gilets jaunes and interregional fairness 10. Fairness from the perspective of an individual or group 11. Fair wages and prices 12. Fairness from the perspective of a caste or race 13. Concluding summary Index

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Book SynopsisThis book presents Martin Shubik's important contribution to the development of game theory, and shows how game theory methods can be used in the study of prices, money and financial institutions.After introducing the reader to his career and the influences which developed his research, Professor Martin Shubik addresses the price system considering issues such as competitive equilibrium, economic exchange and production. He explores the competitive price system and the emergence of money and financial systems to develop a theory of monetary and financial institutions. Specifically, he examines the role of money in the economy using both cooperative and non-cooperative solutions in game theory. Throughout the book Martin Shubik stresses that the value of games, which can be both played and analysed, provides an important link between theory and process and institutional studies.This book will be welcomed by economists, especially those interested in game theory, as well as by money and banking professionals.Trade Review'Martin Shubik has been one of the great pioneers in the application of game theory to economic problems. His work sheds considerable light on fundamental institutions such as the price system and money.' -- Eric Maskin, Harvard University, US'The two volumes of the Selected Essays of Professor Shubik present a recognizably most valuable collection. The earlier publication of Shubik's book Game Theory in the Social Sciences was very much appreciated and won the Lanchester Prize of the Operations Research Society of America. This illustrates how the work of Martin Shubik connects ideas, precision, and methods of mathematics with a real understanding of what are the relevant issues which make an otherwise generic scientific question indeed a question of economic interest and significance (and the same can be said a little more broadly with 'the social sciences' replacing economics). The volumes are of interest because the papers that are included are well-chosen and in particular include interesting collaborations of Shubik with co-authors such as Dubey and Shapley.' -- John Nash, Princeton University, US'Game theory is now a mainstay of a wide range of disciplines within economics and elsewhere. The credit for recognizing its potentiality belongs to a small group of dedicated researchers, of whom one of the liveliest and most influential is Martin Shubik. These essays are a testament to his remarkable insight.' -- Ken Binmore, University College London, UKTable of ContentsContents: Introduction Part I: The Price System Part II: The Theory of Money and Financial Institutions Index

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