Game Theory
 Teacher(s): L.Santos Pinto A.Gizatulina
 Course given in: English
 ECTS Credits: 6 credits
 Schedule: Spring Semester 20182019, 4.0h. course (weekly average)
 séances
 Related programme: Master of Science (MSc) in Economics
ObjectivesThe purpose of this course is to make masters students at UNIL acquainted with the basic solution concepts used to solve games, namely: Dominance, Iterated Deletion of Dominated Strategies, Rationalizability, Nash Equilibrium, Backward Induction, Subgame Perfect Equilibrium, Bayesian Nash Equilibrium, and Perfect Bayesian Equilibrium. In addition, the course also discusses how real people play games, the impact of social preferences on equilibrium outcomes, and nonequilibrium models of behavior in games. Contents1 Introduction 1.1 What is Game Theory? 1.2 Modeling Strategic Interaction: Normal Form and Matrix Form 2 Static Games of Complete Information 2.1 Rationality and Common Knowledge 2.1.1 Dominance in Pure Strategies 2.1.2 Dominant and Dominated Strategy Equilibrium 2.1.3 Evaluating Dominant Strategy Equilibrium 2.2 Iterated Elimination of Strictly Dominated Pure Strategies 2.2.1 Iterated Elimination and Common Knowledge of Rationality 2.2.2 Example: Cournot Duopoly 2.2.3 Evaluating IESDS 2.3 Beliefs, Best Response, and Rationalizability 2.3.1 The Best Response 2.3.2 Beliefs and BestResponse Correspondences 2.3.3 Rationalizability 2.3.4 The Cournot Duopoly Revisited 2.3.5 The “pBeauty Contest” 2.3.6 Evaluating Rationalizability 2.4 Nash Equilibrium in Pure Strategies 2.4.1 PureStrategy Nash Equilibrium in a Matrix 2.4.2 Evaluating the Nash Equilibria Solution 2.4.3 Nash Equilibrium: Some Classic Applications 2.5 Mixed Strategies 2.5.1 Finite Strategy Sets 2.5.2 Continuous Strategy Sets 2.5.3 Beliefs and Mixed Strategies 2.5.4 MixedStrategy Nash Equilibrium 2.5.4.1. Example: Matching Pennies 2.5.4.2. Example: RockPaperScissors 2.5.4.3. Multiple Equilibria: Pure and Mixed 2.5.5 IESDS and Rationalizability Revisited 2.6. Nash’s Existence Theorem 2.7. Refinements 2.7.1 How Can We Justify the Play of a Particular Nash Equilibrium? 2.7.2 Trembling Hand Perfection 2.7.3 Pareto Dominance 2.7.4 Risk Dominance 2.7.5 Evolution 3 Dynamic Games of Complete Information 3.1. The ExtensiveForm Game 3.1.1 Game Trees 3.1.2 Imperfect versus Perfect Information 3.1.3 Pure Strategies 3.1.4 Mixed versus Behavioral Strategies 3.1.5 NormalForm Representation of ExtensiveForm Games 3.2 Credibility and Sequential Rationality 3.2.1. Sequential Rationality and Backward Induction 3.2.2 SubgamePerfect Nash Equilibrium: Concept 3.2.3 SubgamePerfect Nash Equilibrium: Examples 3.2.3.1 The Centipede Game 3.2.3.2 Stackelberg Competition 3.2.3.3 Mutually Assured Destruction 3.2.3.4 TimeInconsistent Preferences 3.3 Multistage Games 3.3.1. Payoffs, Strategies and Conditional Play 3.3.2. SubgamePerfect Equilibria 3.3.3. The OneStage Deviation Principle 3.3.4. Economic Applications: Bank Runs, Trade Policy 3.4. Infinitely Repeated Games 3.4.1. Finitely Repeated Games 3.4.2. Infinitely Repeated Games: SubgamePerfect Equilibria 3.4.3. Applications: Tacit Collusion 3.4.4. Sequential Interaction and Reputation 3.4.4.1. Cooperation as Reputation 3.4.4.2. ThirdParty Institutions as Reputation Mechanisms 3.4.4.3. Reputation Transfers without Third Parties 3.4.5. The Folk Theorem: Almost Anything Goes 3.5 Bargaining Theory 3.5.1 The Cooperative Game Theory Approach 3.5.1.1. Nash’s Solution (Econometrica, 1950) 3.5.2 The NonCooperative Game Theory (or Strategic) Approach: 3.5.2.1 Nash’s Demand Game (Econometrica, 1953) 3.5.2.2 The Ultimatum Bargaining Game 3.5.2.3 RubinsteinStahl Bargaining Model 3.5.3. Application: Legislative Bargaining 3.5.3.1. ClosedRule Bargaining 3.5.3.2 OpenRule Bargaining 4 Static Games of Incomplete Information 4.1 Incomplete Information 4.2 The Notion of Type and Strategy 4.3 Bayesian Updating of Beliefs 4.4 Bayesian Nash Equilibrium 4.5 Economic Application 3: Market Entry 4.6 Economic Application 4: Provision of Public Goods 4.7 Economic Application 5: Auctions 5 Dynamic Games of Incomplete Information 5.1 Introduction to Perfect Bayesian Equilibrium (PBE) 5.1.1 PBE in Dynamic Games of Complete Information 5.1.2 Beliefs and Sequential Rationality 5.1.3 Definition of PBE 5.1.4 Economic Application 6: Market Entry 5.2 PBE in Signaling Games 5.2.1 Example: The BeerQuiche Game 5.3 Multistage Games with Observed Actions and Incomplete Information 5.4 The OneShotDeviation Principle 5.5 Economic Application 7: JobMarket Signaling 6 Behavioral Game Theory 6.1 Introduction 6.2 Ultimatum, Dictator and Trust Games 6.3 Theories of Social Preferences 6.3.1 Fehr and Schmidt (1999) 6.3.2 Charness and Rabin (2002) 6.4 NonEquilibrium Models of Behavior in Games 6.4.1 DominanceSolvable Games 6.4.2 Simple DominanceSolvable Games 6.4.3 The pBeauty Contest 6.4.4 The Cognitive Hierarchy Model 6.4.5.1 Coordination Games 6.4.5.2 The Stag Hunt Game 6.4.5.3 Economic Application 8: Market Entry 6.5 Thinking Steps Models: Discussion ReferencesSteve Tadelis, Game Theory: An Introduction, Princeton University Press, Princeton, New Jersey. Robert Gibbons, Game Theory for Applied Economists, Princeton University Press, Princeton, New Jersey. Geoffrey Jehle and Philip Reny, Advanced Microeconomic Theory, Third Edition Prentice Hall Financial Times. We will cover chapter 8. Martin Osborne and Ariel Rubinstein, A Course in Game Theory, The MIT Press, Cambridge, Massachusetts. We will cover parts of chapter 3. Andreu MasColell, Michael Whinston, and Jerry Green, Microeconomic Theory, Oxford University Press, Oxford, New York. We will cover chapters 7, 8 and 9. Camerer, Colin, Behavioral Game Theory: Experiments in Strategic Interaction, Russell Sage Foundation and Princeton University Press, 2003. We will cover chapter 2 and parts of chapters 5 and 7. EvaluationFirst attempt
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