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

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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.

Author(s): Rodica Branzei, Dinko Dimitrov, Stef Tijs
Series: Lecture Notes in Economics and Mathematical Systems 556
Edition: 1
Publisher: Springer
Year: 2005

Language: English
Pages: 131
City: Berlin; New York
Tags: Game Theory/Mathematical Methods; Game Theory, Economics, Social and Behav. Sciences; Operations Research/Decision Theory; Microeconomics

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