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Chapters in Game Theory. In Honor of Stef Tijs


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.

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1Stochastic Cooperative Games: Theory and Applications1 BYPETERBORM ANDJEROENSUIJS 1.1Introduction1 1.2Cooperative DecisionMaking under Risk5 1.2.1ChanceConstrained Games5 1.2.2Stochastic Cooperative Games with Transfer Pay ments7 1.2.3Stochastic Cooperative Games without Transfer Payments11 1.3Cost Allocation in a Network Tree15 1.4Bankruptcy Problems with Random Estate19 1.5Concluding Remarks22
Sequencing Games: a Survey BYIMMACURIEL, HERBERTHAMERS,ANDFLIPKLIJN 2.1Introduction 2.2Games Related to Sequencing Games 2.3Sequencing Situations and Sequencing Games 2.4On Sequencing Games with Ready Times or Due Dates 2.5On Sequencing Games with Multiple Machines 2.6On Sequencing Games with more Admissible Rearrange ments
Game Theory and the Market BYERIC VANDAMME ANDDAVEFURTH 3.1Introduction 3.2Von Neumann, Morgenstern and Nash 3.3Bargaining
27 29
31 36 40
51 52 57
3.4 3.5 3.6
Markets Auctions Conclusion
61 69 77
On the Number of Extreme Points of the Core of a Trans ferable Utility Game83 BYJEANDERKS ANDJEROENKUIPERS 4.1Introduction83 4.2Main Results85 4.3The Core of a Transferable Utility Game88 4.4Strict Exact Games91 4.5Concluding Remarks94
5Consistency and Potentials in Cooperative TUGames: Sobolev’s Reduced Game Revived99 BYTHEODRIESSEN 5.1Introduction99 5.2Consistency Property for Solutions that Admit a Potential102 5.3a Detailed ExpoConsistency Property for Pseudovalues: sition108 5.4Concluding remarks116 5.5Two technical proofs116
On the Set of Equilibria of a Bimatrix Game: a Survey121 BYMATHIJSJANSEN, PETERJURG,ANDDRIESVERMEULEN 6.1Introduction121 6.2Bimatrix Games and Equilibria124 6.3Some Observations by Nash124 6.4The Approach of Vorobev and Kuhn126 6.5The Approach of Mangasarian and Winkels129 6.6The Approach of Winkels131 6.7The Approach of Jansen133 6.8The Approach of Quintas136 6.9Jurg and JansenThe Approach of 136 6.10The Approach of Vermeulen and Jansen140
Concave and Convex Serial Cost Sharing BYMAURICEKOSTER 7.1Introduction 7.2The Cost Sharing Model 7.3The Convex and the Concave Serial Cost Sharing Rule
Centrality Orderings in Social Networks BYHERMANMONSUUR ANDTONSTORCKEN 8.1Introduction 8.2Examples of Centrality Orderings 8.3Cover Centrality Ordering 8.4Degree Centrality Ordering 8.5Median Centrality Ordering 8.6Independence of the Characterizing Conditions
9The Shapley Transfer Procedure for NTUGames BYGERTJANOTTEN ANDHANSPETERS 9.1Introduction 9.2Main Concepts 9.3Nonemptiness of Transfer Solutions 9.4A Characterization 9.5Applications 9.5.1The Shapley Value 9.5.2The Core 9.5.3The Nucleolus 9.5.4The 9.6Concluding Remarks
10The Nucleolus as Equilibrium Price BYJos POTTERS, HANSREIJNIERSE,ANDANITA VANGELLEKOM 10.1Introduction 10.2Preliminaries 10.2.1 Economies with Indivisible Goods and Money 10.2.2Preliminaries about TUGames 10.3Stable Equilibria 10.4Necessary and SuffiThe Existence of Price Equilibria: cient Conditions 10.5The Nucleolus as Regular Price Vector
143 144 146
157 159 164 168 173 177
183 185 189 192 195 195 196 198 199 202
205 207 208 209 210
216 218
11Network Formation, Costs, and Potential Games BYMARCOSLIKKER ANDANNE VAN DENNOUWELAND 11.1Introduction 11.2Literature Review 11.3Network Formation Model in Strategic Form 11.4Potential Games 11.5Potential Maximizer
12Stochastic GamesContributions to the Theory of BYFRANKTHUIJSMAN ANDKOOSVRIEZE 12.1The Stochastic Game Model 12.2ZeroSum Stochastic Games 12.3GeneralSum Stochastic Games
13Programs and CooperativeLinear (Semi) Infinite Games BYJUDITHTIMMER ANDNATIVIDADLLORCA 13.1Introduction 13.2Semiinfinite Programs and Games 13.2.1Flow games 13.2.2 Linear Production Games 13.2.3 Games Involving Linear Transformation of Products 13.3Infinite Programs and Games 13.3.1Assignment Games 13.3.2 Transportation Games 13.4Concluding remarks
14Population Uncertainty and Equilibrium Selection: Maximum Likelihood Approach BYMARKVOORNEVELD ANDHENKNORDE 14.1Introduction 14.2Preliminaries 14.2.1 Topology 14.2.2Measure Theory 14.2.3Game Theory 14.3Games with Population Uncertainty 14.4Maximum Likelihood Equilibria 14.5Measurability
223 224
228 233 238
247 250 255
267 268 268 270
273 276 276 279 283
a 287
287 289 289 290 291 292 293 297
14.6Random Action Sets 14.7Random Games 14.8Robustness Against Randomization 14.9Weakly Strict Equilibria 14.10Approximate Maximum Likelihood Equilibria
299 300 302 305 308