An Introduction to Game Theory

by Osborne, Martin J.

• ISBN13: 9780195128956
• ISBN10: 0195128958
• eBook ISBN(s): 9780197583067
• Additional ISBN(s): 9780195128963
• Format: Hardcover
• Copyright: 2003-08-07
• Publisher: Oxford University Press
• More Book Details
• Purchase Benefits

Summary

Game theoretic reasoning pervades economic theory and is used widely in other social and behavioral sciences. An Introduction to Game Theory presents the main ideas underlying this theory and shows how it can be used to understand economic, social, political, and biological phenomena. Emphasizing the ideas behind the theory rather than their mathematical expression, it assumes no specific knowledge beyond basic mathematics. It defines all concepts precisely and uses logical reasoning throughout.

Table of Contents

Preface	xi
Introduction	1	(10)
What is game theory?	1	(3)
An outline of the history of game theory	2	(1)
John von Neumann	3	(1)
The theory of rational choice	4	(3)
Coming attractions: interacting decision-makers	7	(4)
Notes	9	(2)
I Games with Perfect Information	11	(260)
Nash Equilibrium: Theory	13	(42)
Strategic games	13	(1)
Example: the Prisoner's Dilemma	14	(4)
Example: Bach or Stravinsky?	18	(1)
Example: Matching Pennies	19	(1)
Example: the Stag Hunt	20	(1)
Nash equilibrium	21	(5)
John F. Nash, Jr.	23	(1)
Studying Nash equilibrium experimentally	24	(2)
Examples of Nash equilibrium	26	(9)
Experimental evidence on the Prisoner's Dilemma	28	(4)
Focal points	32	(3)
Best response functions	35	(10)
Dominated actions	45	(5)
Equilibrium in a single population: symmetric games and symmetric equilibria	50	(5)
Notes	53	(2)
Nash Equilibrium: Illustrations	55	(44)
Cournot's model of oligopoly	55	(8)
Bertrand's model of oligopoly	63	(7)
Cournot, Bertrand, and Nash: some historical notes	69	(1)
Electoral competition	70	(7)
The War of Attrition	77	(3)
Auctions	80	(11)
Auctions from Babylonia to eBay	81	(10)
Accident law	91	(8)
Notes	97	(2)
Mixed Strategy Equilibrium	99	(54)
Introduction	99	(7)
Some evidence on expected payoff functions	104	(2)
Strategic games in which players may randomize	106	(1)
Mixed strategy Nash equilibrium	107	(13)
Dominated actions	120	(2)
Pure equilibria when randomization is allowed	122	(1)
Illustration: expert diagnosis	123	(5)
Equilibrium in a single population	128	(3)
Illustration: reporting a crime	131	(3)
Reporting a crime: social psychology and game theory	133	(1)
The formation of players' beliefs	134	(3)
Extension: finding all mixed strategy Nash equilibria	137	(5)
Extension: games in which each player has a continuum of actions	142	(4)
Appendix: representing preferences by expected payoffs	146	(7)
Notes	150	(3)
Extensive Games with Perfect Information: Theory	153	(28)
Extensive games with perfect information	153	(6)
Strategies and outcomes	159	(2)
Nash equilibrium	161	(3)
Subgame perfect equilibrium	164	(5)
Finding subgame perfect equilibria of finite horizon games: backward induction	169	(12)
Ticktacktoe, chess, and related games	178	(1)
Notes	179	(2)
Extensive Games with Perfect Information: Illustrations	181	(24)
The ultimatum game, the holdup game, and agenda control	181	(6)
Experiments on the ultimatum game	183	(4)
Stackelberg's model of duopoly	187	(5)
Buying votes	192	(5)
A race	197	(8)
Notes	203	(2)
Extensive Games with Perfect Information: Extensions and Discussion	205	(34)
Allowing for simultaneous moves	205	(8)
More experimental evidence on subgame perfect equilibrium	211	(2)
Illustration: entry into a monopolized industry	213	(2)
Illustration: electoral competition with strategic voters	215	(2)
Illustration: committee decision-making	217	(4)
Illustration: exit from a declining industry	221	(4)
Allowing for exogenous uncertainty	225	(6)
Discussion: subgame perfect equilibrium and backward induction	231	(5)
Experimental evidence on the centipede game	234	(2)
Notes	236	(3)
Coalitional Games and the Core	239	(32)
Coalitional games	239	(4)
The core	243	(4)
Illustration: ownership and the distribution of wealth	247	(4)
Illustration: exchanging homogeneous horses	251	(5)
Illustration: exchanging heterogeneous houses	256	(4)
Illustration: voting	260	(3)
Illustration: matching	263	(6)
Matching doctors with hospitals	268	(1)
Discussion: other solution concepts	269	(2)
Notes	270	(1)
II Games with Imperfect Information	271	(88)
Bayesian Games	273	(40)
Motivational examples	273	(5)
General definitions	278	(4)
Two examples concerning information	282	(3)
Illustration: Cournot's duopoly game with imperfect information	285	(4)
Illustration: providing a public good	289	(2)
Illustration: auctions	291	(10)
Auctions of the radio spectrum	300	(1)
Illustration: juries	301	(6)
Appendix: auctions with an arbitrary distribution of valuations	307	(6)
Notes	311	(2)
Extensive Games with Imperfect Information	313	(46)
Extensive games with imperfect information	313	(4)
Strategies	317	(1)
Nash equilibrium	318	(5)
Beliefs and sequential equilibrium	323	(8)
Signaling games	331	(5)
Illustration: conspicuous expenditure as a signal of quality	336	(4)
Illustration: education as a signal of ability	340	(3)
Illustration: strategic information transmission	343	(8)
Illustration: agenda control with imperfect information	351	(8)
Notes	357	(2)
III Variants and Extensions	359	(148)
Strictly Competitive Games and Maxminimization	361	(16)
Maxminimization	361	(3)
Maxminimization and Nash equilibrium	364	(1)
Strictly competitive games	365	(2)
Maxminimization and Nash equilibrium in strictly competitive games	367	(10)
Maxminimization: some history	370	(3)
Empirical tests: experiments, tennis, and soccer	373	(2)
Notes	375	(2)
Rationalizability	377	(16)
Rationalizability	377	(8)
Iterated elimination of strictly dominated actions	385	(3)
Iterated elimination of weakly dominated actions	388	(3)
Dominance solvability	391	(2)
Notes	392	(1)
Evolutionary Equilibrium	393	(26)
Monomorphic pure strategy equilibrium	394	(6)
Evolutionary game theory: some history	399	(1)
Mixed strategies and polymorphic equilibrium	400	(6)
Asymmetric contests	406	(5)
Side-blotched lizards	407	(2)
Explaining the outcomes of contests in nature	409	(2)
Variation on a theme: sibling behavior	411	(3)
Variation on a theme: the nesting behavior of wasps	414	(2)
Variation on a theme: the evolution of the sex ratio	416	(3)
Notes	417	(2)
Repeated Games: The Prisoner's Dilemma	419	(32)
The main idea	419	(2)
Preferences	421	(2)
Repeated games	423	(1)
Finitely repeated Prisoner's Dilemma	424	(2)
Infinitely repeated Prisoner's Dilemma	426	(1)
Strategies in an infinitely repeated Prisoner's Dilemma	426	(2)
Some Nash equilibria of an infinitely repeated Prisoner's Dilemma	428	(3)
Nash equilibrium payoffs of an infinitely repeated Prisoner's Dilemma	431	(6)
Experimental evidence	436	(1)
Subgame perfect equilibria and the one-deviation property	437	(4)
Axelrod's tournaments	439	(2)
Some subgame perfect equilibria of an infinitely repeated Prisoner's Dilemma	441	(5)
Reciprocal altruism among sticklebacks	445	(1)
Subgame perfect equilibrium payoffs of an infinitely repeated Prisoner's Dilemma	446	(3)
Medieval trade fairs	448	(1)
Concluding remarks	449	(2)
Notes	449	(2)
Repeated Games: General Results	451	(14)
Nash equilibria of general infinitely repeated games	451	(4)
Subgame perfect equilibria of general infinitely repeated games	455	(5)
Finitely repeated games	460	(1)
Variation on a theme: imperfect observability	461	(4)
Notes	463	(2)
Bargaining	465	(28)
Bargaining as an extensive game	465	(12)
Illustration: trade in a market	477	(4)
Nash's axiomatic model	481	(8)
Relation between strategic and axiomatic models	489	(4)
Notes	491	(2)
Appendix: Mathematics	493	(14)
Numbers	493	(1)
Sets	494	(1)
Functions	495	(3)
Profiles	498	(1)
Sequences	499	(1)
Probability	499	(6)
Proofs	505	(2)
References	507	(18)
Index	525