Games, theory and applications / L.C. Thomas.

Format:

Book

Author/Creator:

Thomas, L. C.

Language:

English

Subjects (All):

Game theory.

Physical Description:

279 pages : illustrations ; 22 cm

Place of Publication:

Mineola, N.Y. : Dover Publications, 2003.

Summary:

Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to the fundamentals and applications of game theory. It opens with the theory of two-person zero-sum games, two-person non-zero-sum games, and n-person games, at a level between nonmathematical introductory books and technical mathematical game theory books. Succeeding sections focus on a variety of applications -- including introductory explanations of gaming and metagames -- that offer nonspecialists information about new areas of game theory at a comprehensible level. Numerous exercises appear with full solutions, in addition to an extensive bibliography, 80 problems with worked solutions, and more than 30 illustrations useful for the theory of non-zero and n-person games. All readers involved in game theory will find this book of value, as will those interested in the applications of mathematics and in game theory's potential role in matters of economics, operational research, business theory, accounting, marketing, advertising, and related fields.

Contents:

Chapter 1 'The Game's Afoot' 15

1.4 History of game theory 20

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

Chapter 3 Two-Person Non-Zero-Sum Games 53

3.1 Differences between zero and non-zero-sum games 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

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

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

Chapter 6 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

Chapter 7 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

Chapter 8 Evolutionary Games 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

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

Chapter 10 Gaming 223

10.1 What is gaming? 223

10.2 Why do gaming? 224

10.3 Running a gaming experiment 228.

Notes:

" ... a slightly corrected, unabridged republication of the 1968 paperback edition of the work originally published by Ellis Horwood/John Wiley, Chichester, London, in 1984"--T.p. verso.

Includes bibliographical references (pages [265]-274) and indexes.

ISBN:

0486432378

9780486432373

OCLC:

52729155

Online:

Publisher description