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Game Theory

• Teacher(s):
• Course given in: English
• ECTS Credits:
• Schedule: Spring Semester 2018-2019, 4.0h. course (weekly average)
WARNING :   this is an old version of the syllabus, old versions contain   OBSOLETE   data.
•  sessions
• Related programmes:

Objectives

The 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 non-equilibrium models of behavior in games.

Contents

1 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 Best-Response Correspondences

2.3.3 Rationalizability

2.3.4 The Cournot Duopoly Revisited

2.3.5 The “p-Beauty Contest”

2.3.6 Evaluating Rationalizability

2.4 Nash Equilibrium in Pure Strategies

2.4.1 Pure-Strategy 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 Mixed-Strategy Nash Equilibrium

2.5.4.1. Example: Matching Pennies

2.5.4.2. Example: Rock-Paper-Scissors

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 Extensive-Form 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 Normal-Form Representation of Extensive-Form Games

3.2 Credibility and Sequential Rationality

3.2.1. Sequential Rationality and Backward Induction

3.2.2 Subgame-Perfect Nash Equilibrium: Concept

3.2.3 Subgame-Perfect 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 Time-Inconsistent Preferences

3.3 Multistage Games

3.3.1. Payoffs, Strategies and Conditional Play

3.3.2. Subgame-Perfect Equilibria

3.3.3. The One-Stage 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: Subgame-Perfect 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. Third-Party 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 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

3.5.3. Application: Legislative Bargaining

3.5.3.1. Closed-Rule Bargaining

3.5.3.2 Open-Rule 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 Beer-Quiche Game

5.3 Multistage Games with Observed Actions and Incomplete Information

5.4 The One-Shot-Deviation Principle

5.5 Economic Application 7: Job-Market 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 Non-Equilibrium Models of Behavior in Games

6.4.1 Dominance-Solvable Games

6.4.2 Simple Dominance-Solvable Games

6.4.3 The p-Beauty 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

References

Steve 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 Mas-Colell, 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.

Evaluation

First attempt

Exam:
Without exam (cf. terms)
Evaluation:

Gizatulina

Your grade for the first part of the course will consists of: active participation during lectures (10%), namely how actively you ask and answer questions, and present solutions to the homework exercises; the remaining part (90%) will consist of the grade you will obtain during the written exam that will take place during the 7th week of lectures (please make sure that you are present during this week). The written exam will cover the theoretical material as well as exercises from the first part of the course.

Santos-Pinto

Your grade in the second part of the course will be determined on the basis of: participation during lectures (10%), take home problem sets (40%), and presentation of a journal article (50%).

Participation during lectures includes answering and asking questions. If at some point you cannot follow part of the lecture, then you should interrupt me and ask for a clarification (this can also count as participation during lectures).

Take home problem sets are team work from 2 to 3 students. You can work together in all of the problems in a problem set or divide them among the team members. You are free to change teams at any time during the semester (as long as every team has at least 2 and at most 3 students). The grade obtained by your team applies to all team members.

The journal article can be selected from any field of economics but must use one of the basic game theory equilibrium concepts covered during the first 20 lectures of the course. Each student should prepare a presentation of the article with more or less the following guidelines: (1) research question, (2) motivation, (3) the model, (5) main result(s), (6) sketch of proof(s) of main result(s), (7) economic intuition behind the main result(s), (8) discussion of assumptions or methodology, and (9) conclusion. The deadline for choosing the journal article is the 30th of April. So, you must send me an email between the 19th of February and the 30th of April with your choice. If two or more students choose the same article, then the article will be attributed to the student who chose first. The other student(s) will have to choose another article. The sooner you choose your favorite article the more likely it is for you to get it.

Retake

Exam:
Written 3h00 hours
Documentation:
Not allowed
Calculator:
Not allowed
Evaluation:

If you fail the course you will have to take a final exam. The final exam is written and closed-book. The duration of the final exam is 3 hours. In case of a retake the retake exam determines 100% of your final grade.

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