Game Theory: A Critical Introduction

by Hargreaves-Heap; Shaun

• ISBN13: 9780415250955
• ISBN10: 0415250951
• Edition: 2nd
• Format: Paperback
• Copyright: 2004-04-08
• Publisher: Routledge

Summary

Game theory now provides the theoretical underpinning for a multitude of courses in economics worldwide. The speed of these developments has been remarkable and they have constituted something of a revolution. Indeed, the basic tenets of game theory have now begun to colonize other social sciences and its proponents have been unified in claiming its natural basis as a rational theory of society. But the technical demands of the subject and the lack of clarity of many commentators' explanations have been a problem for many. This second edition of Shaun Hargreaves-Heap and Yanis Varoufakis's classic text strips away the mystique and lets the student make his or her own mind up. This new edition: * lays bear the philosophy behind game theory and explains all its major concepts * conducts a clear explanation and careful analysis of all the main 'games', such as repeated games and the prisoner's dilemma, as well as less well-trodden topics such as experimental games and issues ofrationality * introduces and analyses new areas of game theory such as "evolutionary games" and "Psychological games" Retaining the most popular features from the original edition, this latest version offers improved pedagogy, new questions for discussion, new chapters on the latest developments as well as a host of new examples. A new generation of students of game theory will grow to appreciate this superb text whilst fans of the first edition will eagerly devour this long-awaited update.

Author Biography

Shaun P. Hargreaves Heap is Professor of Economics at the University of East Anglia, UK.

Table of Contents

List of boxes	xi
Preface	xiii
Overview	1	(40)
Introduction	1	(6)
Why study game theory?	1	(1)
What is game theory?	2	(1)
Why this book?	3	(1)
Why a second book?	4	(2)
The rest of this chapter	6	(1)
The assumptions of game theory	7	(26)
Individual action is instrumentally rational	7	(20)
Common knowledge of rationality (CKR)	27	(1)
Common priors	28	(3)
Action within the rules of the games	31	(2)
Liberal individualism, the state and game theory	33	(3)
Methodological individualism	33	(2)
Game theory's contribution to liberal individualism	35	(1)
A guide to the rest of the book	36	(4)
Three classic games: Hawk--Dove, Co-ordination and the Prisoner's Dilemma	36	(2)
Chapter-by-chapter guide	38	(2)
Conclusion	40	(1)
The Elements of Game Theory	41	(39)
Introduction	41	(3)
The representation of strategies, games and information sets	44	(3)
Pure and mixed strategies	44	(1)
The normal form, the extensive form and the information set	45	(2)
Dominance reasoning	47	(5)
Rationalisable beliefs and actions	52	(6)
The successive elimination of strategically inferior moves	52	(4)
Rationalisable strategies and their connection with Nash's equilibrium	56	(2)
Nash equilibrium	58	(10)
John Nash's beautiful idea	58	(2)
Consistently aligned beliefs, the hidden Principle of Rational Determinacy and the Harsanyi--Aumann doctrine	60	(1)
Some objections to Nash: Part I	61	(7)
Nash equilibrium in mixed strategies	68	(10)
The scope and derivation of Nash equilibria in mixed strategies	68	(5)
The reliance of NEMS on CAB and the Harsanyi doctrine	73	(2)
Aumann's defence of CAB and NEMS	75	(3)
Conclusion	78	(2)
Problems	79	(1)
Battling Indeterminacy: Refinements of Nash's Equilibrium in Static and Dynamic Games	80	(47)
Introduction	80	(1)
The stability of Nash equilibria	81	(9)
Trembling hand perfect Nash equilibria	81	(4)
Harsanyi's Bayesian Nash equilibria and his defence of NEMS	85	(5)
Dynamic games	90	(16)
Extensive form and backward induction	90	(2)
Subgame perfection, Nash and CKR	92	(4)
Sequential equilibria	96	(3)
Bayesian learning, sequential equilibrium and the importance of reputation	99	(4)
Signalling equilibria	103	(3)
Further refinements	106	(5)
Proper equilibria	106	(2)
Forward induction	108	(3)
Some logical objections to Nash, Part II	111	(7)
A critique of subgame perfection	111	(3)
A negative rejoinder (based on the Harsanyi--Aumann doctrine)	114	(1)
A positive rejoinder (based on sequential equilibrium)	115	(2)
Summary: out-of-equilibrium beliefs, patterned trembles and consistency	117	(1)
Conclusion	118	(9)
The status of Nash and Nash refinements	118	(1)
In defence of Nash	119	(3)
Why has game theory been attracted `so uncritically' to Nash?	122	(3)
Problems	125	(2)
Bargaining Games: Rational Agreements, Bargaining Power and the Social Contract	127	(45)
Introduction	127	(4)
Credible and incredible talk in simple bargaining games	131	(4)
John Nash's generic bargaining problem and his axiomatic solution	135	(15)
The bargaining problem	135	(2)
Nash's solution -- an example	137	(3)
Nash's solution as an equilibrium of fear	140	(6)
Nash's axiomatic account	146	(2)
Do the axioms apply?	148	(2)
Ariel Rubinstein and the bargaining process: the return of Nash backward induction	150	(14)
Rubinstein's solution to the bargaining problem	150	(2)
A proof of Rubinstein's theorem	152	(8)
The (trembling hand) defence of Rubinstein's solution	160	(3)
A final word on Nash, trembling hands and Rubinstein's bargaining solution	163	(1)
Justice in political and moral philosophy	164	(6)
The negative result and the opening to Rawls and Nozick	165	(3)
Procedures and outcomes (or `means' and ends) and axiomatic bargaining theory	168	(2)
Conclusion	170	(2)
Problems	171	(1)
The Prisoner's Dilemma: The Riddle of Co-Operation and Its Implications For Collective Agency	172	(39)
Introduction: the state and the game that popularised game theory	172	(3)
Examples of hidden Prisoner's Dilemmas and free riders in social life	175	(5)
Some evidence on how people play the Prisoner's Dilemma and free rider games	180	(5)
Explaining co-operation	185	(6)
Kant and morality: is it rational to defect?	185	(1)
Altruism	186	(1)
Inequality aversion	187	(2)
Choosing a co-operative disposition instrumentally	189	(2)
Conditional co-operation in repeated Prisoner's Dilemmas	191	(14)
Tit-for-Tat in Axelrod's tournament	191	(1)
Tit-for-Tat as a Nash equilibrium strategy when the horizon is unknown	192	(2)
Spontaneous public good provision	194	(2)
The Folk Theorem and Indeterminacy in indefinitely repeated games	196	(6)
Does a finite horizon wreck co-operation? The theory and the evidence	202	(3)
Conclusion: co-operation and the State in Liberal theory	205	(6)
Rational co-operation?	205	(1)
The debate in Liberal political theory	206	(3)
The limits of the Prisoner's Dilemma	209	(1)
Problems	209	(2)
Evolutionary Games: Evolution, Games and Social Theory	211	(56)
Introduction	211	(9)
The origins of Evolutionary Game Theory	212	(2)
Evolutionary stability and equilibrium: an introduction	214	(6)
Symmetrical evolution in homogeneous populations	220	(7)
Static games	220	(3)
Dynamic games	223	(4)
Evolution in heterogeneous populations	227	(21)
Asymmetrical (or two-dimensional) evolution and the demise of Nash equilibria in mixed strategies	227	(5)
Does Evolutionary Game Theory apply to humans as well as it does to birds, ants, etc.? An experiment with two-dimensional evolution in the Hawk-Dove game	232	(4)
Multi-dimensional evolution and the conflict of conventions	236	(5)
The origin of conventions and the challenge to methodological individualism	241	(4)
The politics of mutations: conventions, inequality and revolt	245	(2)
Discriminatory conventions: a brief synopsis	247	(1)
Social evolution: power, morality and history	248	(16)
Social versus natural selection	248	(3)
Conventions as covert social power	251	(1)
The evolution of predictions into moral beliefs: Hume on morality	252	(3)
Gender, class and functionalism	255	(3)
The evolution of predictions into ideology: Marx against morality	258	(6)
Conclusion	264	(3)
Problems	266	(1)
Psychological Games: Demolishing the Divide Between Motives and Beliefs	267	(35)
Introduction	267	(1)
Different types of `other regarding' motives	268	(7)
The `other' regarding motives of Homo Economicus	268	(1)
Beliefs as predictions and as motives	269	(6)
The power of normative beliefs	275	(17)
Fairness equilibria	275	(6)
Computing fairness equilibria	281	(2)
An assessment of Rabin	283	(2)
An alternative formulation linking entitlements to intentions	285	(4)
Team thinking	289	(3)
Psychology and evolution	292	(7)
On the origins of normative beliefs: an adaptation to experience	292	(1)
On the origins of normative beliefs: the resentment-aversion versus the subversion-proclivity hypotheses	293	(6)
Conclusion: shared praxes, shared meanings	299	(3)
Problems	301	(1)
Postscript	302	(2)
Answers to problems	304	(30)
Notes	334	(14)
Bibliography	348	(11)
Name index	359	(3)
Subject index	362