Christophe Crombez

Crombez: Applied Game Theory.

1

Applied Game Theory

Introduction

Crombez: Applied Game Theory.

2

What is Game Theory?

• a way of analyzing strategic interactions • appropriate to study situations in which several people take decisions, and o their decisions affect each other’s payoffs • equivalent of decision theory o

Crombez: Applied Game Theory.

3

Course Objectives

• introduce you to game theory

to understand papers that use it, and o develop game-theoretical models yourselves • the focus is on solution concepts o theory o exercises o a few applications o

Crombez: Applied Game Theory.

4

Contents

• Basic equilibrium concepts

Nash equilibria o Subgame perfection o Sequential equilibria • Applications o Bargaining o Entry deterrence o Repeated games o

Crombez: Applied Game Theory.

5

Practicalities

• Five meetings • Text Book: Kreps, A Course in Microeconomic Theory, Chapters 11-15 • Slides on Toledo • Homeworks • Exam: in January, written, open book, exercises

Crombez: Applied Game Theory.

6

Applied Game Theory

Modeling Competitive Situations

Crombez: Doctoral Seminar.

7

Outline

• • • • •

Decision Trees Game Trees (Extensive Forms) Formalities Normal Forms (Strategic Forms) Mixed Strategies

Kreps: Chapter 11

Crombez: Doctoral Seminar.

8

Decision Trees

• • • •

Choice/decision nodes Chance nodes Branches A chance node precedes a choice node iff the uncertainty represented by that chance node resolves in the mind of the decision maker prior to the time at which the choice must be made.

Crombez: Doctoral Seminar.

9

Game Trees

• • • •

Nature Payoffs Information Sets If someone learns something (a move by nature or by another player) prior to making a decision, the node representing what is learned must precede the node where the decision is taken.

Crombez: Doctoral Seminar.

10

Formalities

• An extensive form representation of a noncooperative

game consists of o a list of players o a game tree o an assignment of decision nodes to players or nature o lists of actions available at each decision node o a correspondence between immediate successors of each decision node and available actions

Crombez: Doctoral Seminar.

11

information sets o an assignment of payoffs for each players to terminal nodes o probability assessments over the initial nodes and over the actions at any node that is assigned to nature • Each node other than the initial nodes has one immediate predecessor. o

Crombez: Doctoral Seminar.

12

• Information Sets

o

o

o

o

each node belongs to one information set a player remembers at any point whether he moved previously any two nodes in an information set have the same player moving a player is faced with the same available actions at any two nodes in an information set

Crombez: Doctoral Seminar.

13

• Simultaneous Moves • Precedence and Information Sets • Perfect Recall o o

a player may not forget what he did earlier a player may not forget what he knew earlier

Crombez: Doctoral Seminar.

14

Normal Forms

• Strategies

specify which actions players take in every information set assigned to them • Strategy Profiles combinations of strategies for the various players • Reduced Normal Forms elimination of equivalent strategies

Crombez: Doctoral Seminar.

15

Mixed Strategies

• Mixed Strategies are probability distributions over pure strategies. • Behaviorally Mixed Strategies mix-as-you-go

Crombez: Doctoral Seminar.

16

Applied Game Theory

Solution Concepts for Noncooperative Games

Crombez: Doctoral Seminar.

17

Outline

• • • • • • • •

Dominance Solvable Games Backwards Induction Nash Equilibrium Equilibria in Mixed Strategies Obvious Ways to Play Games Subgame Perfection Sequential Equilibrium More Refinements Kreps: Chapter 12

Crombez: Doctoral Seminar.

18

Dominance Solvable...