Models in Cooperative Game Theory: Crisp, Fuzzy, and Multi-Choice Games

Rodica Branzei, Dinko Dimitrov, Stef Tijs354026082X, 9783540260820, 9783540285090

This book investigates models in cooperative game theory in which the players have the possibility to cooperate partially. In a crisp game the agents are either fully involved or not involved at all in coperation with some other agents, while in a fuzzy game players are allowed to cooperate with infinite many different participation levels, varying from non-cooperation to full cooperation. A multi-choice game describes the intermediate case in which each player may have a fixed number of activity levels. Different set and one-point solution concepts for these games are presented. The properties of these solution concepts and their interrelations on several classes of crisp, fuzzy, and multi-choice games are studied. Applications of the investigated models to many economic situations are indicated as well.

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Table of contents :
Preliminaries….Pages 5-11
Cores and Related Solution Concepts….Pages 13-21
The Shapley Value and the τ -Value….Pages 23-30
Classes of Cooperative Crisp Games….Pages 31-44
Preliminaries….Pages 49-52
Solution Concepts for Fuzzy Games….Pages 53-66
Convex Fuzzy Games….Pages 67-87
Fuzzy Clan Games….Pages 89-100
Preliminaries….Pages 105-107
Solution Concepts for Multichoice Games….Pages 109-119
Classes of Multichoice Games….Pages 121-128