Game Theory and its Applications in the Social and Biological Sciences

Description

Andrew Coleman provides an accessible introduction to the fundamentals of mathematical gaming and other major applications in social psychology, decision theory, economics, politics, evolutionary biology, philosophy, operational research and sociology. The primary aim of this book is to provide a critical survey of the essential ideas of game theory and the findings of experimental research on strategic interaction. In addition, I have reported some new experiments using lifelike simulations of familiar kinds of strategic interactions, and included discussions of recent applications of game theory to the study of voting, the theory of evolution, and moral philosophy. The time has (alas) long since passed when a single person could reasonably hope to be an expert on all branches of game theory or on all of its applications, and I have not attempted to achieve the impossible. But I thought it worthwhile, none the less, to aim for a fairly comprehensive coverage of important topics, with particular emphasis on those that seemed to be most relevant to naturally occurring strategic interactions. Game theory and the experimental gaming tradition have grown up in relative isolation from each other. Game theorists, in general, remain largely oblivious of the empirical studies that have been inspired by the theory, and experimental investigators have tended to assume that the nuts and bolts of the theory do not concern them. Both parties are the losers from this divorce, and I have therefore tried to contribute towards a reconciliation by examining in detail, for the first time in a single volume, both sides of the story. Cover Title Contents Preface to the First Edition Preface to the Second Edition Part I: Background 1. Introduction 1.1 Intuitive background 1.1.1 Head On 1.1.2 Price War 1.1.3 Angelo and Isabella 1.2 Abstract models: basic terminology 1.3 Skill, chance, and strategy 1.4 Historical background 1.5 Summary 2. One-person games 2.1 Games against Nature 2.2 Certainty 2.3 Risk 2.4 Expected utility theory 2.5 Uncertainty 2.5.1 Insufficient reason 2.5.2 Maximax 2.5.3 Maximin 2.5.4 Minimax regret 2.6 Summary 3. Coordination games and the minimal social situation 3.1 Strategic collaboration 3.2 Coordination games 3.3 The minimal social situation 3.4 The multi-person minimal social situation 3.5 Summary Part II: Theory and empirical evidence 4. Two-person zero-sum games 4.1 Strictly competitive games 4.2 Extensive and normal forms 4.3 Games with saddle points: Nash equilibria 4.4 Games without saddle points 4.5 Dominance and admissibility 4.6 Methods for finding solutions 4.7 Ordinal payoffs and incomplete information 4.8 Summary 5. Experiments with strictly competitive games 5.1 Ideas behind experimental games 5.2 Empirical research on non-saddle-point games 5.3 Empirical research on saddle-point games 5.4 Framing effects 5.5 Critique of experimental gaming 5.6 Summary 6. Two-person mixed-motive games: informal game theory 6.1 Mixed-motive games 6.2 Subgame perfect and trembling-hand equilibria 6.3 Classification of 2 X 2 mixed-motive games 6.4 Leader 6.5 Battle of the Sexes 6.6 Chicken 6.7 Prisoner's Dilemma 6.8 Comparison of archetypal 2 x 2 games 6.9 Theory of meta games 6.10 Two-person cooperative games: bargaining solutions 6.10.1 Maximin bargaining solution 6.10.2 Nash bargaining solution 6.10.3 Raiffa-Kalai-Smorodinsky bargaining solution 6.11 Summary 7. Experiments with Prisoner's Dilemma and related games 7.1 The experimental gaming literature 7.2 Strategic structure 7.3 Payoffs and incentives 7.4 Communication effects 7.5 Programmed strategies 7.6 Axelrod's computer tournaments 7.7 Sex differences and cross-cultural studies 7.8 Attribution effects 7.9 Framing effects 7.10 Summary 8. Multi-person cooperative games: coalition formation 8.1 N-person cooperative games 8.2 Characteristic function and imputation 8.3 Core and stable set 8.4 Harold Pinter's The Caretaker 8.5 Shapley value 8.6 Kernel, nucleolus, and least core 8.7 Coalition-predicting theories 8.7.1 Equal excess theory 8.7.2 Caplow's theory 8.7.3 Minimal winning coalition theory 8.7.4 Minimum resource theory 8.8 Experiments on coalition formation 8.9 Summary 9. Multi-person non-cooperative games and social dilemmas 9.1 N-person non-cooperative games: Nash equilibria 9.2 The Chain-store paradox and backward induction 9.3 Auction games and psychological traps 9.4 Social dilemmas: intuitive background 9.4.1 The "invisible hand" and voluntary wage restraint 9.4.2 Conservation of natural resources 9.4.3 The tragedy of the commons 9.5 Formalization of social dilemmas 9.6 Theory of compound games 9.7 Empirical research on social dilemmas 9.7.1 Group size effects 9.7.2 Communication effects 9.7.3 Individual differences and attribution effects 9.7.4 Payoff and incentive effects 9.7.5 Framing effects 9.8 Summary Part III: Applications 10. Social choice and strategic voting 10.1 Background 10.2 Alternatives, voters, preferences 10.3 Voting procedures 10.4 Voting paradoxes 10.5 Arrow's impossibility theorem 10.6 Proportional representation: single transferable vote 10.7 Strategic (tactical) voting 10.8 Sophisticated voting 10.9 Empirical evidence of strategic voting 10.10 Summary 11. Theory of evolution: strategic aspects 11.1 Historical background 11.2 Strategic evolution and behavioural ecology 11.3 Animal conflicts and evolutionarily stable strategies 11.4 An improved multi-person game model 11.5 Empirical evidence 11.6 Summary 12. Game theory and philosophy 12.1 Relevance of game theory to practical problems 12.2 Rationality in games 12.2.1 Coordination games 12.2.2 Prisoner's Dilemma games 12.3 Newcomb's problem 12.4 Kant's categorical imperative 12.5 Plato, Hobbes, Rousseau: social contract theories 12.6 Evolution and stability of moral principles 12.7 Summary Appendix: A simple proof of the minimax theorem A.1 Introductory remarks A.2 Preliminary formalization A.3 The minimax theorem A.4 Proof A.5 Remark References Index