Osborne M.J. An Introduction to Game Theory

Oxford University Press – 2003, 685 pages
ISBN: 0195128958, 9780195128956Game-theoretic reasoning pervades economic theory and is used widely in other social and behavioral sciences. An Introduction to Game Theory, by Martin J. Osborne, presents the main principles of game theory and shows how they can be used to understand economic, social, political, and biological phenomena. The book introduces in an accessible manner the main ideas behind the theory rather than their mathematical expression. All concepts are defined precisely, and logical reasoning is used throughout. The book requires an understanding of basic mathematics but assumes no specific knowledge of economics, political science, or other social or behavioral sciences.
Coverage includes the fundamental concepts of strategic games, extensive games with perfect information, and coalitional games; the more advanced subjects of Bayesian games and extensive games with imperfect information; and the topics of repeated games, bargaining theory, evolutionary equilibrium, rationalizability, and maxminimization. The book offers a wide variety of illustrations from the social and behavioral sciences and more than 280 exercises. Each topic features examples that highlight theoretical points and illustrations that demonstrate how the theory may be used. Explaining the key concepts of game theory as simply as possible while maintaining complete precision, An Introduction to Game Theory is ideal for undergraduate and introductory graduate courses in game theory.Each chapter ends with notes.What is Game Theory?
The Theory of Rational Choice
Coming Attractions: Interacting Decision-MakersGames with Perfect InformationNash Equilibrium: Theory
Strategic Games
Example: The Prisoner's Dilemma
Example: Bach or Stravinsky?
Example: Matching Pennies
Example: The Stag Hunt
Nash Equilibrium
Examples of Nash Equilibrium
Best Response Functions
Dominated Actions
Equilibrium in a Single Population: Symmetric Games and Symmetric Equilibria
Nash Equilibrium: Illustrations
Cournot's Model of Oligopoly
Bertrand's Model of Oligopoly
Electoral Competition
The War of Attrition
Auctions
Accident Law
Mixed Strategy EquilibriumStrategic Games in Which Players May Randomize
Mixed Strategy Nash Equilibrium
Dominated Actions
Pure Equilibria When Randomization is Allowed
Illustration: Expert Diagnosis
Equilibrium in a Single Population
Illustration: Reporting a Crime
The Formation of Players' Beliefs
Extension: Finding All Mixed Strategy Nash Equilibria
Extension: Games in Which Each Player Has a Continuum of Actions
Appendix: Representing Preferences by Expected Payoffs
Extensive Games with Perfect Information: Theory
Extensive Games with Perfect Information
Strategies and Outcomes
Nash Equilibrium
Subgame Perfect Equilibrium
Finding Subgame Perfect Equilibria of Finite Horizon Games: Backward Induction
Extensive Games With Perfect Information: Illustrations
The Ultimatum Game, the Holdup Game, and Agenda Control
Stackelberg's Model of Duopoly
Buying Votes
A Race
Extensive Games With Perfect Information: Extensions and Discussion
Allowing for Simultaneous Moves
Illustration: Entry into a Monopolized Industry
Illustration: Electoral Competition with Strategic Voters
Illustration: Committee Decision-Making
Illustration: Exit from a Declining Industry
Allowing for Exogenous Uncertainty
Discussion: Subgame Perfect Equilibrium and Backward Induction
Coalitional Games and the Core
Coalitional Games
The Core
Illustration: Ownership and the Distribution of Wealth
Illustration: Exchanging Homogeneous Horses
Illustration: Exchanging Heterogeneous Houses
Illustration: Voting
Illustration: Matching
Discussion: Other Solution ConceptsGames with Imperfect InformationMotivational Examples
General Definitions
Two Examples Concerning Information
Illustration: Cournot's Duopoly Game with Imperfect Information
Illustration: Providing a Public Good
Illustration: Auctions
Illustration: Juries
Appendix: Auctions with an Arbitrary Distribution of Valuations
Extensive Games with Imperfect Information
Extensive Games with Imperfect Information
Strategies
Nash Equilibrium
Beliefs and Sequential Equilibrium
Signaling Games.
Illustration: Conspicuous Expenditure as a Signal of Quality
Illustration: Education as a Signal Of Ability
Illustration: Strategic Information Transmission
Illustration: Agenda Control with Imperfect InformationVariants and ExtensionsStrictly Competitive Games and Maxminimization
Maxminimization
Maxminimization and Nash Equilibrium
Strictly Competitive Games
Maxminimization and Nash Equilibrium in Strictly Competitive Games
Rationalizability
Rationalizability
Iterated Elimination of Strictly Dominated Actions
Iterated Elimination of Weakly Dominated Actions
Dominance Solvability
Evolutionary Equilibrium
Monomorphic Pure Strategy Equilibrium
Mixed Strategies and Polymorphic Equilibrium
Asymmetric Contests
Variation on a Theme: Sibling Behavior
Variation on a Theme: The Nesting Behavior of Wasps
Variation on a Theme: The Evolution of the Sex Ratio
Repeated Games: The Prisoner's Dilemma
The Main Idea
Preferences
Repeated Games
Finitely Repeated Prisoner's Dilemma
Infinitely Repeated Prisoner's Dilemma
Strategies in an Infinitely Repeated Prisoner's Dilemma
Some Nash Equilibria of an Infinitely Repeated Prisoner's Dilemma
Nash Equilibrium Payoffs of an Infinitely Repeated Prisoner's Dilemma
Subgame Perfect Equilibria and the One-Deviation Property
Some Subgame Perfect Equilibria of an Infinitely Repeated Prisoner's Dilemma
Subgame Perfect Equilibrium Payoffs of an Infinitely Repeated Prisoner's Dilemma
Concluding Remarks
Repeated Games: General Results
Nash Equilibria of General Infinitely Repeated Games
Subgame Perfect Equilibria of General Infinitely Repeated Games
Finitely Repeated Games
Variation on a Theme: Imperfect Observability
Bargaining
Bargaining as an Extensive Game
Illustration: Trade in a Market
Nash's Axiomatic Model
Relation Between Strategic and Axiomatic ModelsAppendix: Mathematics
Numbers
Sets
Functions
Profiles
Sequences
Probability
Proofs