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Fuzzy Cooperative Games

Cooperation with Vague Expectations

  • Book
  • © 2001

Overview

Authors:
  1. Milan Mareš

    1. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic

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  • Elementary introduction to a methodologically new view on the mathematical model of cooperation motivated by the fuzzy idea of its participants about the expected outcomes and profits
  • Illustration of technical results by numerous examples
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 72)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XII
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  2. Preliminaries

    1. Front Matter

      Pages 1-3
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    2. Introduction

      • Milan Mareš
      Pages 5-8

    3. Fuzzy Quantities

      • Milan Mareš
      Pages 9-15

    4. Deterministic Coalition Games

      • Milan Mareš
      Pages 17-31

    5. Vagueness and Its Processing

      • Milan Mareš
      Pages 33-34

  3. Fuzzy Bargaining with Side-Payments

    1. Front Matter

      Pages 35-38
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    2. Fuzzy Additivity and Related Topics

      • Milan Mareš
      Pages 39-54

    3. Fuzzy Core and Effective Coalitions

      • Milan Mareš
      Pages 55-66

    4. Fuzzy Convexity

      • Milan Mareš
      Pages 67-77

    5. Fuzzy Balancedness

      • Milan Mareš
      Pages 79-87

    6. Fuzzy Shapley Value

      • Milan Mareš
      Pages 89-93

  4. Fuzzy Bargaining Without Side-Payments

    1. Front Matter

      Pages 95-99
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    2. Fuzzy Superoptimum

      • Milan Mareš
      Pages 101-109

    3. Fuzzy and Imputational Additivity-Like Relations

      • Milan Mareš
      Pages 111-123

    4. Fuzzy Core and Effectivity in Games Without Side-Payments

      • Milan Mareš
      Pages 125-134

  5. Alternative Approaches

    1. Front Matter

      Pages 135-137
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    2. Linear Coalition Games

      • Milan Mareš
      Pages 139-146

    3. A Modified Model of Domination and Superoptimum

      • Milan Mareš
      Pages 147-151

    4. Strategic Background of Fuzzy Cooperation

      • Milan Mareš
      Pages 153-161
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Keywords

About this book

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.

Authors and Affiliations

  • Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic

    Milan Mareš

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