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## Game Theory

• Enseignant(s):
• Titre en français: Théorie des Jeux
• Cours donné en: anglais
• Crédits ECTS:
• Horaire: Semestre de printemps 2020-2021, 4.0h. de cours (moyenne hebdomadaire)
WARNING :   this is an old version of the syllabus, old versions contain   OBSOLETE   data.
•  séances
•  site web du cours
• Formations concernées:

### Objectifs

The purpose of this course is to make masters students at UNIL acquainted with Game Theory and some of its applications.

We will study 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.

### Contenus

1 Introduction

1.1 What is Game Theory?

1.2 Modeling Strategic Interaction

1.2.1 Normal Form versus Extensive Form Representation

1.2.2 Complete/Incomplete vs Perfect/Imperfect Information

2 Static Games of Complete Information

2.1 Introduction

2.2 Mixed Strategies

2.2 Dominated Strategies

2.3 Iterated Deletion of Dominated Strategies

2.4 Behavioral Assumptions Behind Iterated Deletion of Dominated Strategies

2.5 Rationalizability

2.6 Rationalizability and Iterated Deletion of Dominated Strategies

2.7 Nash Equilibrium

2.7.1 Introduction

2.7.2 Definition

2.7.3 How Do we Find Pure Strategy Nash Equilibria?

2.7.4 How Can we Find Mixed Strategy Nash Equilibria?

2.7.5 Behavioral Assumptions behind Nash Equilibrium

2.7.6 Nash Equilibrium and Rationalizability

2.8 How Can We Justify the Play of a Particular Nash Equilibrium?

2.8.1 Weak Dominance

2.8.2 Trembling Hand Perfection

2.8.3 Pareto Dominance

2.8.4 Risk Dominance

2.8.5 Evolution

3 Dynamic Games of Complete Information

3.1 Games of Perfect Information and Backward Induction

3.1.1 Backward Induction (BI)

3.1.2 Behavioral Assumptions behind the Solution Concept BI

3.1.3 Examples

3.2 Games of Imperfect Information and Subgame Perfection

3.2.1 Subgame Perfect Nash Equilibrium (SPNE)

3.2.2 General Procedure to find SPNE in Finite Games

3.2.3 Economic Application 1: Bank Runs

3.2.4 Economic Application 2: Trade Policy

3.3 Formal Definition of Strategy and SPNE

3.3.1 Game Tree Representation, Strategy

3.3.2 Game Tree Representation

3.3.3 Strategies in Extensive Form Games

3.3.4 Equilibria in Extensive Form Games

3.4 Multistage Games with Observed Actions and Complete Information

3.4.1 Finitely Repeated Games

3.4.2 The One-Stage-Deviation-Criterion

3.4.3 Infinitely Repeated Games

3.4.3.1 Introduction

3.4.3.2 Grim Trigger

3.4.3.3 A Variation on Grim Trigger

3.4.3.4 Tit for Tat

3.4.3.5 Folk Theorems

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 Non-Cooperative 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 Rubinstein-Stahl Bargaining Model

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: Incomplete Information Battle of Sexes

4.6 Economic Application 4: Market Entry

4.7 Economic Application 5: Provision of Public Goods

4.8 Economic Application 6: The Market for Used Cars

4.8.1 Gresham’s Law

4.8.2 Akerlof’s Market for Lemons: Introduction

4.8.3 Akerlof’s Market for Lemons: Binary Type Case

4.8.4 Akerlof’s Market for Lemons: Continuous Type Case

4.8.5 Akerlof’s Market for Lemons: Remedy

5 Dynamic Games of Incomplete Information

5.1 Perfect Bayesian Equilibrium (PBE)

5.1.1 Introduction

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 7: Market Entry

5.2 PBE in Signaling Games

5.2.1 Example: The Beer-Quiche Game

5.3 Multistage Games with Observed Actions and Incomplete Information

5.4 The One-Shot-Deviation Principle

5.5 Economic Application 8: Job-Market Signaling

### Références

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 chapters 7 and 8.

Martin Osborne and Ariel Rubinstein, A Course in Game Theory, The MIT Press, Cambridge, Massachusetts. We will cover parts of chapter 3.

Andreu Mas-Colell, Michael Whinston, and Jerry Green, Microeconomic Theory, Oxford University Press, Oxford, New York. We will cover chapters 7, 8 and 9.

### Pré-requis

The skills and knowledge of the HEC MScE microeconomics are required for this course.

### Evaluation

#### 1ère tentative

Examen:
Sans examen (cf. modalités)
Evaluation:

Your grade in the course will be determined on the basis of: 60 % take home problem sets and 40 % presentation of a journal article.

#### Rattrapage

Examen:
Sans examen (cf. modalités)
Evaluation:

Your grade in the course will be determined on the basis of: 60 % take home problem sets and 40 % presentation of a journal article.

Existing passing grades for each part of the evaluation can be carried over.

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