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Playing for RealGame Theory$
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Ken Binmore

Print publication date: 2007

Print ISBN-13: 9780195300574

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780195300574.001.0001

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 Teaming Up

 Teaming Up

Chapter:
(p.521) 18 Teaming Up
Source:
Playing for Real
Author(s):

Ken Binmore (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195300574.003.0018

This chapter offers a brief survey of the theory of coalition formation introduced by Von Neumann and Morgenstern. The coalitional form of a game is defined and discussed. The idea of the core of a game is explained, together with its application to Walrasian equilibria. The Condorcet paradox is used in the game Odd-Man-Out to illustrate the myopia attributed to players by the core concept. This serves as an introduction to the idea of a Von Neumann and Morgenstern stable set. The Three-Cake Game is used to illustrate both the core, stable sets, and the Shapley value. The progress made in applying the Nash program in this area — for example, to the case of one seller and several buyers — is reviewed.

Keywords:   Von Neumann and Morgenstern, coalitional form, transferable utility, Condorcet paradox, Odd-Man-Out, stable sets, Three-Cake Game, Shapley value, bargaining pit model, telephone bargaining model

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