Fun and Games A Text on Game Theory

Contents Teaching Guide Introduction What Is Game Theory About? Where Is Game Theory Coming From? Where Is Game Theory Going To? What Can Game Theory Do for Us? Conclusion 1. Winning Out 1.1 Introduction 1.2 The Rules of the Game 1.3 Strategies 1.4 Zermelo's Algorithm 1.5 Nim 1.6 Hex 1.7 Chess 1.8 Rational Play? Conflict and Cooperation Exercises 2. Taking Chances 2.1 Introduction 2.2 Lotteries 2.3 Game Values 2.4 Duel 2.5 Parcheesi 2.6 Exercises 3. Accounting for Tastes 3.1 Rational Preferences 3.2 Utility Functions 3.3 Russian Roulette 3.4 Making Risky Choices 3.5 Utility Scales 3.6 The Noble Savage 3.7 Exercises 4. Getting Paid Off 4.1 Payoffs 4.2 Bimatrix Games 4.3 Matrices 4.4 Vectors 4.5 Hyperplanes 4.6 Domination 4.7 Russian Roulette Again 4.8 Exercises 5. Making Deals 5.1 Introduction 5.2 Convexity 5.3 Cooperative Payoff Regions 5.4 The Bargaining Set 5.5 Nash Bargaining Solutions 5.6 Dividing the Dollar 5.7 Cooperative and Noncooperative Games 5.8 Bargaining Models 5.9 Exercises 6. Mixing Things Up 6.1 Introduction 6.2 Minimax and Maximin 6.3 Safety First 6.4 Mixed Strategies 6.5 Zero-Sum Games 6.6 Separating Hyperplanes 6.7 Battleships 6.8 The Inspection Game Nash Threat Game Exercises 7. Keeping Your Balance 7.1 Reaction Curves 7.2 Oligopoly and Perfect Competition 7.3 Equilibrium Selection 7.4 Nash Demand Game 7.5 Pre-play Negotiation 7.6 Pre-play Randomization 7.7 When Do Nash Equilibria Exist? 7.8 Hexing Brouwer 7.9 Exercises 8. Repeating Yourself 8.1 Reciprocity 8.2 Repeating a Zero-Sum Game 8.3 Repeating the Prisoners' Dilemma 8.4 Infinite Repetitions 8.5 Social Contract 8.6 Exercises 9. Adjusting to Circumstances 9.1 Spontaneous Order 9.2 Bounded Rationality 9.3 Economic Libration 9.4 Social Libration 9.5 Biological Libration 9.6 Evolution Stability 9.7 The Evolution of Cooperation 9.8 Exercises 10. Knowing Your Place 10.1 Bob's Your Uncle 10.2 Knowledge 10.3 Possibility 10.4 Information Sets 10.5 Bayesian Updating 10.6 Common Knowledge 10.7 Agreeing to Disagree? Common Knowledge in Game Theory Exercises 11. Knowing Who to Believe 11.1 Complete and Incomplete Information 11.2 Typecasting 11.3 Bayesian Equilibrium 11.4 Continuous Random Variables 11.5 Duopoly with Incomplete Information 11.6 Purification 11.7 Auctions and Mechanism Design 11.8 Assessment Equilibrium 11.9 More Agreeing to Disagree 11.10 Exercises 12. Bluffing It Out 12.1 Poker 12.2 Conditional Probability Densities 12.3 Borel's Poker Model 12.4 Von Neuman's Poker Model 12.5 Why Bluff? 12.6 Nash and Shapley's Poker Model 12.7 Conclusion Answers IndexBinmore, Kenneth is the author of 'Fun and Games A Text on Game Theory' with ISBN 9780669246032 and ISBN 0669246034.