Fuzzy Cooperative Games: Cooperation with Vague Expectations

ISBN-13: 9783790824896 / Angielski / Miękka / 2010 / 177 str.

Milan Mares

Opis

The present book deals with coalition games in which expected pay-offs are only vaguely known. In fact, this idea about vagueness of expectations ap- pears to be adequate to real situations in which the coalitional bargaining anticipates a proper realization of the game with a strategic behaviour of players. The vagueness being present in the expectations of profits is mod- elled by means of the theory of fuzzy set and fuzzy quantities. The fuzziness of decision-making and strategic behaviour attracts the attention of mathematicians and its particular aspects are discussed in sev- eral works. One can mention in this respect in particular the book "Fuzzy and Multiobjective Games for Conflict Resolution" by Ichiro Nishizaki and Masatoshi Sakawa (referred below as 43]) which has recently appeared in the series Studies in Fuzziness and Soft Computing published by Physica-Verlag in which the present book is also apperaing. That book, together with the one you carry in your hands, form in a certain sense a complementary pair. They present detailed views on two main aspects forming the core of game theory: strategic (mostly 2-person) games, and coalitional (or cooperative) games. As a pair they offer quite a wide overview of fuzzy set theoretical approaches to game theoretical models of human behaviour.

Spis treści

1 Introduction.- 2 Fuzzy Quantities.- 3 Deterministic Coalition Games.- 4 Vagueness and Its Processing.- 5 Fuzzy Additivity and Related Topics.- 6 Fuzzy Core and Effective Coalitions.- 7 Fuzzy Convexity.- 8 Fuzzy Balancedness.- 9 Fuzzy Shapley Value.- 10 Fuzzy Superoptimum.- 11 Fuzzy and Imputational Additivity-Like Relations.- 12 Fuzzy Core and Effectivity in Games Without Side-Payments.- 13 Linear Coalition Games.- 14 A Modified Model of Domination and Superoptimum.- 15 Strategic Background of Fuzzy Cooperation.- 16 Generation of Fuzzy Quantities.- V Concluding Remarks.- References.

Blurb

The book deals with the mathematical model of coalitional cooperation based on vague knowledge of its expected outcomes. This reality is described by the model of coalitional game (with or without transferable utility) in which the expected pay-offs are represented by fuzzy quantities or by fuzzy sets of real-valued vectors. This approach to the fuzziness in the bargaining is new and completes the existing literature on this topic by alternative views. The presentation does not demand deeper than elementary knowledge of linear algebra and some related topics. The book can be used as an introduction to the subject presenting basic concepts and results.