Borm / Peters Chapters in Game Theory

In honor of Stef Tijs
2002
ISBN: 978-0-306-47526-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 31, 328 Seiten

Reihe: Theory and Decision Library C

Chapters in Game Theory has been written on the occasion of the 65th birthday of Stef Tijs, who can be regarded as the godfather of game theory in the Netherlands. The contributors all are indebted to Stef Tijs, as former Ph.D. students or otherwise. The book contains fourteen chapters on a wide range of subjects. Some of these can be considered surveys while other chapters present new results: most contributions can be positioned somewhere in between these categories. The topics covered include: cooperative stochastic games, noncooperative stochastic games, sequencing games, games arising form linear (semi-) infinite programming problems, network formation, costs and potential games, potentials and consistency in transferable utility games, the nucleolus and equilibrium prices, population uncertainty and equilibrium selection, cost sharing, centrality in social networks, extreme points of the core, equilibrium sets of bimatrix games, game theory and the market, and transfer procedures for nontransferable utility games. Both editors did their Ph.D with Stef Tijs, while he was affiliated with the mathematics department of the University of Nijmegen.

Autoren/Hrsg.

Borm, Peter

Peters, H. J.

Inhaltsverzeichnis

1;Preface;6
2;About Stef Tijs;7
3;About this book;7
4;About the authors;10
5;Contents;14
6;Chapter 1 Stochastic Cooperative Games: Theory and Applications;19
6.1;1.1 Introduction;19
6.2;1.2 Cooperative Decision-Making under Risk;23
6.2.1;1.2.1 Chance-Constrained Games;23
6.2.2;1.2.2 Stochastic Cooperative Games with Transfer Payments;25
6.2.3;1.2.3 Stochastic Cooperative Games without Transfer Payments;29
6.3;1.3 Cost Allocation in a Network Tree;33
6.4;1.4 Bankruptcy Problems with Random Estate;37
6.5;1.5 Concluding Remarks;40
6.6;Appendix;41
6.7;References;43
7;Chapter 2 Sequencing Games: a Survey;45
7.1;2.1 Introduction;45
7.2;2.2 Games Related to Sequencing Games;47
7.3;2.3 Sequencing Situations and Sequencing Games;49
7.4;2.4 On Sequencing Games with Ready Times or Due Dates;54
7.5;2.5 On Sequencing Games with Multiple Machines;58
7.6;2.6 On Sequencing Games with more Admissible Rearrangements;63
7.7;References;66
8;Chapter 3 Game Theory and the Market;69
8.1;3.1 Introduction;69
8.2;3.2 Von Neumann, Morgenstern and Nash;70
8.3;3.3 Bargaining;75
8.4;3.4 Markets;79
8.5;3.5 Auctions;87
8.6;3.6 Conclusion;95
8.7;References;96
9;Chapter 4 On the Number of Extreme Points of the Core of a Transferable Utility Game;101
9.1;4.1 Introduction;101
9.2;4.2 Main Results;103
9.3;4.3 The Core of a Transferable Utility Game;106
9.4;4.4 Strict Exact Games;109
9.5;4.5 Concluding Remarks;112
9.6;References;114
10;Chapter 5 Consistency and Potentials in Cooperative TU- Games: Sobolev’s Reduced Game Revived;117
10.1;5.1 Introduction;117
10.2;5.2 Consistency Property for Solutions that Admit a Potential;120
10.3;5.3 Consistency Property for Pseudovalues: a Detailed Exposition;126
10.4;5.4 Concluding remarks;134
10.5;5.5 Two technical proofs;134
10.6;References;137
11;Chapter 6 On the Set of Equilibria of a Bimatrix Game: a Survey;139
11.1;6.1 Introduction;139
11.2;6.2 Bimatrix Games and Equilibria;142
11.3;6.3 Some Observations by Nash;142
11.4;6.4 The Approach of Vorobev and Kuhn;144
11.5;6.5 The Approach of Mangasarian and Winkels;147
11.6;6.7 The Approach of Jansen;151
11.7;6.8 The Approach of Quintas;154
11.8;6.9 The Approach of Jurg and Jansen;154
11.9;6.10 The Approach of Vermeulen and Jansen;158
11.10;References;159
12;Chapter 7 Concave and Convex Serial Cost Sharing;161
12.1;7.1 Introduction;161
12.2;7.2 The Cost Sharing Model;162
12.3;7.3 The Convex and the Concave Serial Cost Sharing Rule;164
12.4;References;172
13;Chapter 8 Centrality Orderings in Social Networks;175
13.1;8.1 Introduction;175
13.2;8.2 Examples of Centrality Orderings;177
13.3;8.3 Cover Centrality Ordering;182
13.4;8.4 Degree Centrality Ordering;186
13.5;8.5 Median Centrality Ordering;191
13.6;8.6 Independence of the Characterizing Conditions;195
13.7;References;197
14;Chapter 9 The Shapley Transfer Procedure for NTU- Games;201
14.1;9.1 Introduction;201
14.2;9.2 Main Concepts;203
14.3;9.3 Nonemptiness of Transfer Solutions;207
14.4;9.4 A Characterization;210
14.5;9.5 Applications;213
14.5.1;9.5.1 The Shapley Value;213
14.5.2;9.5.2 The Core;214
14.5.3;9.5.3 The Nucleolus;216
14.5.4;9.5.4 The t-Value;217
14.6;9.6 Concluding Remarks;220
14.7;References;220
15;Chapter 10 The Nucleolus as Equilibrium Price;223
15.1;10.1 Introduction;223
15.2;10.2 Preliminaries;225
15.2.1;10.2.1 Economies with Indivisible Goods and Money;226
15.2.2;10.2.2 Preliminaries about TU-Games;227
15.3;10.3 Stable Equilibria;228
15.4;10.4 The Existence of Price Equilibria: Necessary and Sufficient Conditions;234
15.5;10.5 The Nucleolus as Regular Price Vector;236
15.6;References;240
16;Chapter 11 Network Formation, Costs, and Potential Games;241
16.1;11.1 Introduction;241
16.2;11.2 Literature Review;242
16.3;11.3 Network Formation Model in Strategic Form;246
16.4;11.4 Potential Games;251
16.5;11.5 Potential Maximizer;256
16.6;References;262
17;Chapter 12 Contributions to the Theory of Stochastic Games;265
17.1;12.1 The Stochastic Game Model;265
17.2;12.2 Zero-Sum Stochastic Games;268
17.3;12.3 General-Sum Stochastic Games;273
17.4;References;279
18;Chapter 13 Linear (Semi-) Infinite Programs and Cooperative Games;285
18.1;13.1 Introduction;285
18.2;13.2 Semi-infinite Programs and Games;286
18.2.1;13.2.1 Flow games;286
18.2.2;13.2.2 Linear Production Games;288
18.2.3;13.2.3 Games Involving Linear Transformation of Products;291
18.3;13.3 Infinite Programs and Games;294
18.3.1;13.3.1 Assignment Games;294
18.3.2;13.3.2 Transportation Games;297
18.4;13.4 Concluding remarks;301
18.5;References;302
19;Chapter 14 Population Uncertainty and Equilibrium Selection: a Maximum Likelihood Approach;305
19.1;14.1 Introduction;305
19.2;14.2 Preliminaries;307
19.2.1;14.2.1 Topology;307
19.2.2;14.2.2 Measure Theory;308
19.2.3;14.2.3 Game Theory;309
19.3;14.3 Games with Population Uncertainty;310
19.4;14.4 Maximum Likelihood Equilibria;311
19.5;14.5 Measurability;315
19.6;14.6 Random Action Sets;317
19.7;14.8 Robustness Against Randomization;320
19.8;14.9 Weakly Strict Equilibria;323
19.9;14.10 Approximate Maximum Likelihood Equilibria;326
19.10;References;331