Economics and the theory of games 1st Edition by Fernando Vega Redondo 0521772516 9780521772518

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ISBN 10: 0521772516

ISBN 13: 9780521772518

Author: Fernando Vega-Redondo

This textbook offers a systematic, self-contained account of the main contributions of modern game theory and its applications to economics. Starting with a detailed description of how to model strategic situations, the discussion proceeds by studying basic solution concepts, their main refinements, games played under incomplete information, and repeated games. For each of these theoretical developments, there is a companion set of applications that cover the most representative instances of game-theoretic analysis in economics, e.g. oligopolistic competition, public goods, coordination failures, bargaining, insurance markets, implementation theory, signaling and auctions. The theory and applications covered in the first part of the book fall under the so-called ‘classical’ approach to game theory, which is founded on the paradigm of players’ unlimited rationality. The second part shifts towards topics that no longer abide by that paradigm. This leads to the study of topics such as the interplay between evolution and rationality.

Economics and the theory of games 1st Table of contents:

CHAPTER 1 Theoretical framework

1.1 Introduction and examples

1.2 Representation of a game in extensive form

1.2.1 Formalization

1.2.2 Examples

1.3 Representation of a game in strategic form

1.3.1 Formalization

1.3.2 Examples

1.4 Mixed extension of a game

1.5 Mixed and behavioral strategies

1.5.1 Formal relationship

1.5.2 Perfect recall and strategic equivalence

1.6 Representation of a game in coalitional form

Summary

Exercises

CHAPTER 2 Strategic-form analysis: theory

2.1 Dominance and iterative dominance

2.2 Nash equilibrium

2.2.1 Formalization and discussion

2.2.2 Examples

2.2.3 Existence: informal discussion

2.3 Zero-sum bilateral games

2.4 Nash equilibrium: formal existence results

2.5 Strong and coalition-proof equilibria

2.6 Correlated equilibrium

2.7 Rationalizability

Summary

Exercises

CHAPTER 3 Strategic-form analysis: applications

3.1 Oligopoly (I): static models

3.1.1 Cournot model

3.1.2 Bertrand model

3.2 Mechanism design (I): efficient allocation of public goods

3.2.1 Subscription mechanism

3.2.2 An efficient mechanism

3.3 Mechanism design (II): Nash implementation

3.3.1 Formulation of the design problem

3.3.2 Partial characterization

3.4 Markets (I): macroeconomic coordination failures

Summary

Exercises

CHAPTER 4 Refinements of Nash equilibrium: theory

4.1 Introduction

4.2 Refinements excluding “incredible threats”: examples

4.3 Subgame-perfect equilibrium

4.4 Weak perfect Bayesian equilibrium

4.5 Refinements excluding “untenable beliefs”: examples

4.5.1 Deviations interpreted as mistakes

4.5.2 Deviations interpreted as alternative theories

4.5.3 Deviations interpreted as signals

4.6 Sequential equilibrium

4.7 Perfect and proper equilibria

4.8 Strategic-form refinements

Summary

Exercises

CHAPTER 5 Refinements of Nash equilibrium: applications

5.1 Oligopoly (II): sequential moves

5.1.1 Stackelberg model

5.1.2 Price competition under capacity constraints

5.2 Markets (II): decentralized price formation

5.2.1 Bilateral strategic bargaining

5.2.2 Strategic bargaining in a population context

5.3 Oligopoly (III): differentiated products

5.4 Mechanism design (III): efficient allocation of an indivisible object

Summary

Exercises

CHAPTER 6 Incomplete information: theory

6.1 Introduction and examples

6.2 Bayesian games

6.2.1 Harsanyi formalization

6.2.2 Examples

6.3 Bayes-Nash equilibrium

6.3.1 Formalization

6.3.2 Examples

6.4 Signaling games

6.4.1 Introduction and examples

6.4.2 Formalization

6.4.3 Signaling equilibrium

6.4.4 Examples

6.5 Mixed strategies, revisited: a purification approach

6.6 Forward induction

6.6.1 Intuitive criterion: motivation

6.6.2 A formal definition for signaling games

Summary

Exercises

CHAPTER 7 Incomplete information: applications

7.1 Markets (III): signaling in the labor market

7.2 Markets (IV): insurance markets and adverse selection

7.3 Mechanism design (IV): one-sided auctions

7.3.1 First-price auctions

7.3.2 Optimal auction design: the revelation principle

7.4 Mechanism design (V): buyer–seller trade

7.4.1 Double auctions

7.4.2 The impossibility of efficient trade

Summary

Exercises

CHAPTER 8 Repeated interaction: theory

8.1 Introduction and examples

8.2 Repeated games: basic theoretical framework

8.3 Folk theorems: Nash equilibrium

8.3.1 Infinite horizon

8.3.2 Finite horizon

8.4 Reputation and “irrationality”: informal discussion

8.5 Folk theorems: subgame-perfect equilibrium

8.5.1 Infinite horizon

8.5.2 Finite horizon

8.6 Reputation and “irrationality”: formal analysis

8.6.1 A common time horizon

8.6.2 Different time horizons

Summary

Exercises

CHAPTER 9 Repeated interaction: applications

9.1 Oligopoly (IV): intertemporal collusion in a Cournot scenario

9.1.1 Perfect observation

9.1.2 Imperfect observation

9.2 Oligopoly (V): intertemporal collusion in a Bertrand scenario

9.2.1 Perfect observation

9.2.2 Imperfect observation

9.3 Markets (V): efficiency wages and unemployment

9.3.1 Perfect observation

9.3.2 Imperfect observation

Summary

Exercises

CHAPTER 10 Evolution and rationality

10.1 Introduction

10.2 Static analysis

10.2.1 Theoretical framework

10.2.2 Evolutionarily stable strategy

10.2.3 ESS and equilibrium

10.2.4 Examples

10.3 Basic dynamic analysis

10.3.1 Replicator dynamics

10.3.2 Replicator dynamics and equilibrium

10.3.3 Examples

10.4 Evolution in social environments

10.4.1 Social evolutionary systems

10.4.2 Payoff monotonicity and rationality

10.4.3 Examples

10.5 Evolution of cooperation: an example

Summary

Exercises

CHAPTER 11 Learning to play

11.1 Introduction

11.2 Reinforcement learning

11.2.1 Positive reinforcement and fixed aspirations

11.2.2 General reinforcement and flexible aspirations

11.3 Static perceptions and myopic behavior

11.3.1 The strategic framework

11.3.2 Learning by imitation

11.3.3 Better- and best-response adjustment

11.4 Memory, expectations, and foresight

11.4.1 Fictitious play

11.4.2 Smooth fictitious play

11.4.3 Rational learning

Summary

Exercises

CHAPTER 12 Social learning and equilibrium selection

12.1 Introduction

12.2 Evolutionary games: theoretical framework

12.2.1 Strategic setup

12.2.2 Learning dynamics

12.3 Evolutionary games: alternative scenarios

12.3.1 Bilateral coordination games

12.3.2 Minimum-effort game

12.3.3 Cournot oligopoly

12.4 Stochastic stability and equilibrium selection

12.4.1 Bilateral coordination games under global interaction

12.4.2 Bilateral coordination games under local interaction

12.4.3 Bilateral coordination games under centralized interaction

12.4.4 Minimum-effort game

12.4.5 Cournot oligopoly

12.5 Experimental evidence

12.5.1 Minimum-effort game

12.5.2 Cournot oligopoly

12.6 Perturbed Markov processes: basic concepts and techniques

12.6.1 Markov chains

12.6.2 A canonical model

12.6.3 Stochastic stability and long-run dynamics

12.6.4 Stochastic stability: mathematical techniques

12.7 Reinforcement learning with flexible aspirations

12.7.1 Prisoner’s dilemma

12.7.2 Pure-coordination games

12.7.3 Experimental evidence: prisoner’s dilemma

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