Advertisement

Cooperative Games on Combinatorial Structures

  • Jesús Mario Bilbao

Part of the Theory and Decision Library book series (TDLC, volume 26)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jesús Mario Bilbao
    Pages 1-25
  3. Jesús Mario Bilbao
    Pages 27-63
  4. Jesús Mario Bilbao
    Pages 65-87
  5. Jesús Mario Bilbao
    Pages 89-109
  6. Jesús Mario Bilbao
    Pages 111-127
  7. Jesús Mario Bilbao
    Pages 129-155
  8. Jesús Mario Bilbao
    Pages 157-180
  9. Jesús Mario Bilbao
    Pages 181-203
  10. Jesús Mario Bilbao
    Pages 205-236
  11. Jesús Mario Bilbao
    Pages 237-252
  12. Jesús Mario Bilbao
    Pages 253-270
  13. Jesús Mario Bilbao
    Pages 271-301
  14. Back Matter
    Pages 303-326

About this book

Introduction

The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations in which two or more players can make coalitions and obtain prizes and penalties. This approach to situations of competition and cooperation was given in the seminal treatise by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Cooperative game theory has succeeded in providing many applications of game theory.
In this volume, games defined on combinatorial structures will be analyzed, i.e. a set system over a set of players. In many situations the author will work in a closure space. Examples of closure operators are the spanning operator of linear algebra and all convex hull operators.
Chapters 1-4 constitute a review of mathematical concepts from Cooperative Game Theory, Graph Theory, Linear and Integer Programming, Combinatorial Optimization, Discrete Convex Analysis and Computational Complexity. The table of contents is a short guide to the topics and methods covered in this book. In Chapters 11 and 12, several notebooks are presented with the system Mathematica by Wolfram in the contexts of the packages DiscreteMath (Skiena) and Cooperative (Carter). There will also be found in the book several research projects. These are intended to offer new ideas that the reader should consider with caution.
This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences. In addition, it will be especially useful for professionals who are interested in models for understanding and managing conflicts: management and operational research scientists, political and military scientists, and professional negotiators.

Keywords

calculus cooperative games economic theory game theory linear algebra linear optimization optimization

Authors and affiliations

  • Jesús Mario Bilbao
    • 1
  1. 1.University of SevilleSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-4393-0
  • Copyright Information Kluwer Academic Publishers 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-6976-9
  • Online ISBN 978-1-4615-4393-0
  • Series Print ISSN 0924-6126
  • Buy this book on publisher's site