Coherent Structures and Simple Games / Edition 1

by K.G. Ramamurthy

Overview

The motivation for this monograph can be traced to a seminar on Simple Games given by Professor S.H. Tijs of the Catholic University at Nijmegen way back in 1981 or 1982 at the Delhi campus of the Indian Statistical Institute. As an ap­ plied statistician and a consultant in quality control, I was naturally interested in Reliability Theory. I was aquainted with topics in reliability like coherent systems, importance of components etc., mainly through Barlow and Proschan's book. At the seminar given by Professor Tijs, I noticed the striking similarity between the concepts in reliability and simple games and this kindled my interest in simple games. When I started going deep into the literature of simple games, I noticed that a number of concepts as well as results which were well known in game theory were rediscovered much later by researchers in reliability. Though the conceptual equivalence of coherent structures and simple games has been noticed quite early, it is not that much well known. In fact, the theoretical developments have taken place practically independent of each other, with considerable duplication of research effort. The basic objective of this monograph is to unify some of the concepts and developments in reliability and simple games so as to avoid further duplication.

Product Details

ISBN-13:	9780792308690
Publisher:	Springer Netherlands
Publication date:	09/30/1990
Series:	Theory and Decision Library C , #6
Edition description:	1990
Pages:	162
Product dimensions:	6.14(w) x 9.21(h) x 0.24(d)

Table of Contents

1 Coherent Structures.- 1.1 Introduction.- 1.2 Structure Functions.- 1.3 Coherent Structures.- 1.4 Minimal Path and Cut Sets.- 1.5 Simple Form of Structure Functions.- 2 Simple Games.- 2.1 Introduction.- 2.2 Simple Games.- 2.3 Blocking Systems.- 2.4 Some Descriptive Results.- 2.5 Matroidal Games.- 3 Importance of Components and Power of Players.- 3.1 Introduction.- 3.2 The Reliability Function.- 3.3 Measures of Importance or Power.- 3.4 An Unified Approach.- 4 Modules and Modular Sets.- 4.1 Introduction.- 4.2 Contraction and Restriction.- 4.3 Characterization of Modular Sets.- 4.4 Properties of Modular Sets.- 4.5 Computational Aspects.- 5 Social Choice.- 5.1 Introduction.- 5.2 Impossibility Theorem.- Notation.

Editorial Reviews

Having noted that many of the concepts well known in game theory were rediscovered much later by researchers in reliability theory, and continue to be explored separately, with much duplication of effort, in the two fields, Ramamurthy, from the Indian Statistical Institute in New Delhi, shows the equivalence of coherent structure and simple games, and the parallel or analogous relation between other sets of concepts. Among the chapters are discussions of components and power of players, modules and modular sets, and social choice. The treatment is highly mathematical. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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