Models in Cooperative Game Theory

ISBN-13: 9783642096761 / Angielski / Miękka / 2010 / 204 str.

Rodica Branzei; Dinko Dimitrov; Stef Tijs

Opis

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 cooperation 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. The second edition is highly enlarged and contains new results and additional sections in the different chapters as well as one new chapter.

Recenzje

From the reviews:

"This small book can be very interesting for readers who want to study further generalizations of the classical topic on cooperative games. It investigates the classical cooperative games with transferable utility and some game models in which the players have the possibility to cooperate partially, that is, fuzzy games and multichoice games. The book is written very clearly, being a rich review of the most essential notions and theorems (with proofs) in these topics." (Tadeusz Radzik, Zentralblatt MATH, Vol. 1079, 2006)

From the reviews of the second edition:

"This is the second edition of the highly regarded monograph on cooperative games by Branzei, Dimitrov and Tijs. ... The 128 references add to the value of the presentation. This monograph will bring the reader to almost everything currently known about cooperative games with transferable utility in coalition form." (Roy Gardner, Zentralblatt MATH, Vol. 1142, 2008)

"This book deals with cooperative game theory, probably the most important class of game in game theory. ... The book is concise. In each part a goal is proposed and developed without digressions or comments. Finally, the book provides a wide-ranging bibliography where the different aspects can be found treated in depth. For all these reasons, I find the book an appealing guide for researchers and practitioners in cooperative game theory with fuzzy coalitions or multi-choice cooperative games." (Pedro Miranda, Mathematical Reviews, Issue 2012 a)

Spis treści

Cooperative Games with Crisp Coalitions.- Preliminaries.- Cores and Related Solution Concepts.- The Shapley Value, the ?-value, and the Average Lexicographic Value.- Egalitarianism-based Solution Concepts.- Classes of Cooperative Crisp Games.- Cooperative Games with Fuzzy Coalitions.- Preliminaries.- Solution Concepts for Fuzzy Games.- Convex Fuzzy Games.- Fuzzy Clan Games.- Multi-Choice Games.- Preliminaries.- Solution Concepts for Multi-Choice Games.- Classes of Multi-Choice Games.