Games, Theory and Applications

by L. C. Thomas

Overview

This text opens with the theory of 2-person zero-sum games, 2-person non-zero sum games, and n-person games, at a level between non-mathematical introductory books and technical mathematical game theory books. Includes introductory explanations of gaming and meta games. Includes numerous exercises anbd problems with solutions and over 30 illustrations. 1986 edition.

Product Details

ISBN-13:	9780486143736
Publisher:	Dover Publications
Publication date:	12/13/2012
Sold by:	Barnes & Noble
Format:	eBook
Pages:	288
File size:	14 MB
Note:	This product may take a few minutes to download.

Table of Contents

	Author's Preface	11
	Glossary of Symbols	13
Chapter 1	'The Game's Afoot'	15
1.1	What is a game?	15
1.2	Examples of games	16
1.3	Terminology of game theory	17
1.4	History of game theory	20
	Problems	21
Chapter 2	Two-Person Zero-Sum Games	23
2.1	Extensive form	23
2.2	Normal form	27
2.3	Maximin criterion	29
2.4	Mixed strategies	30
2.5	Minimax theorem	33
2.6	Domination	34
2.7	Worthwhile strategies	37
2.8	Solutions of 2 x m games	37
2.9	Equilibrium pairs	42
2.10	Games with perfect information	44
2.11	Solving n x m games	45
2.12	Further reading	48
	Problems	50
Chapter 3	Two-Person Non-Zero-Sum Games	53
3.1	Differences between zero and non-zero-sum games	53
3.2	Examples	53
3.3	Equilibrium pairs and maximin-maximin pairs	56
3.4	Sketch proof of Nash's theorem	57
3.5	How to find equilibrium pairs (Swastika Method)	59
3.6	Solution concepts of non-zero-sum games	61
3.7	Cooperative games	64
3.8	Bargaining or negotiation set	66
3.9	Nash's bargaining axioms	67
3.10	Maximin bargaining solution	72
3.11	Threat bargaining solution	75
3.12	Further reading	81
	Problems	81
Chapter 4	N-Person Games	85
4.1	Non-cooperative games	85
4.2	Characteristic function	86
4.3	Strategic equivalence of characteristic functions	89
4.4	Imputations	90
4.5	The core	91
4.6	Stable sets	94
4.7	Nucleolus	99
4.8	Shapley value	101
4.9	Other solution concepts	104
4.10	Further reading	107
	Problems	108
Chapter 5	Market Games and Oligopoly	112
5.1	Edgeworth market games	112
5.2	[1,1]-market game	112
5.3	[M,N]-market game	114
5.4	[1,N]-market game	116
5.5	[N,N]-market game	117
5.6	Duopoly and oligopoly	118
5.7	Cournot equilibrium	119
5.8	Other solution concepts in duopoly	121
5.9	Quantity model, symmetric games and oligopoly theory	125
5.10	Further reading	126
	Problems	126
Chapter 6	Metagames	129
6.1	Objectives of metagames	129
6.2	Metagames and metaequilibria	130
6.3	Metarationality theorem	134
6.4	Examples of metagame analysis	136
6.5	Symmetric metaequilibria	139
6.6	Analysis of options	141
6.7	Analysis of options applied to market strategy	142
6.8	Further reading	145
	Problems	147
Chapter 7	Multi-Stage Games	150
7.1	Multi-stage games	150
7.2	Stochastic games, recursive games and supergames	152
7.3	Discounted stochastic games	153
7.4	Existence of value	154
7.5	Advertising example	157
7.6	Bounds on value iteration	158
7.7	Recursive games	160
7.8	Solution of recursive games	161
7.9	Examples of recursive games	162
7.10	Supergames	164
7.11	Relationship between supergames and metagames: oligopoly example	165
7.12	Further reading	168
	Problems	170
Chapter 8	Evolutionary Games	176
8.1	Introduction	176
8.2	Evolutionary stable strategies (ESS)	177
8.3	Examples of evolutionary games	178
8.4	Properties of evolutionary stable strategies	181
8.5	How to find evolutionary stable strategies	182
8.6	War of attrition	184
8.7	Dynamic evolutionary games	187
8.8	Stability in dynamic evolutionary games	189
8.9	Evolutionary stable strategies in multi-type games	192
8.10	Further reading	195
	Problems	196
Chapter 9	Bidding and Auctions	200
9.1	Types of auctions	200
9.2	Dutch auction--discrete bids and known valuations	202
9.3	Dutch auction--continuous bids and known valuations	207
9.4	English auction--known valuations	209
9.5	Auctions with unknown valuations	211
9.6	Auctions of two or more objects	214
9.7	Horse market auctions	216
9.8	Further reading	220
	Problems	221
Chapter 10	Gaming	223
10.1	What is gaming?	223
10.2	Why do gaming?	224
10.3	Running a gaming experiment	228
10.4	Further reading	231
	Solutions to problems	233
	References	265
	Index	275
	Name index	278