The Cooperative Game Theory of Networks and Hierarchies

ISBN-13: 9783642263156 / Angielski / Miękka / 2012 / 270 str.

Robert P. Gilles

Opis

This book details standard concepts in cooperative game theory with applications to the analysis of social networks and hierarchical authority organizations. It covers the multi-linear extension, the Core, the Shapley value, and the cooperative potential.

Recenzje

From the reviews:

"It is worthwhile to emphasize that this book is very clearly and rigorously written. ... chapters is accompanied by an appendix section containing proofs of the main theorems, and by a problem section, allowing this book to be used as a textbook for an advanced graduate course on game theory. ... this book can also be seen as a very valuable position for game theorists." (Tadeusz Radzik, Zentralblatt MATH, Vol. 1198, 2010)

"In The cooperative game theory of networks and hierarchies, Gilles has written an introduction to cooperative game theory and its applications to hierarchical structures that serves equally well as a graduate level text and a primer for the researcher wanting a concise but highly readable account of recent work in this field. ... the author has provided extensive and thoughtful discussion of the assumptions and applicability of these models to economic and other institutions." (Jennifer M. Wilson, Mathematical Reviews, Issue 2012 f)

Spis treści

Cooperative Game Theory.- The Core of a Cooperative Game.- Axiomatic Value Theory.- The Cooperative Potential.- Directed Communication Networks.- Cooperative Theories of Hierarchical Organizations.

Blurb

The book brings together an overview of standard concepts in cooperative game theory with applications to the analysis of social networks and hierarchical authority organizations. The standard concepts covered include the multi-linear extension, the Core, the Shapley value, and the cooperative potential. Also discussed are the Core for a restricted collection of formable coalitions, various Core covers, the Myerson value, value-based potentials, and share potentials. Within the context of social networks this book discusses the measurement of centrality and power as well as allocation rules such as the Myerson value and hierarchical allocation rules. For hierarchical organizations, two basic approaches to the exercise of authority are explored; for each approach the allocation of the generated output is developed. Each chapter is accompanied by a problem section, allowing this book to be used as a textbook for an advanced graduate course on game theory.