Cooperative Games on Combinatorial Structures

The aim of this text 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 are analyzed, that is, 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. 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). These are intended to offer new ideas that the reader should consider with caution.This book should 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 should be 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.