Refinements of the \(\beta\)-core and the strong equilibrium and the Aumann proposition
type: Item
instance of: scholarly article
title: Refinements of the \(\beta\)-core and the strong equilibrium and the Aumann proposition
zbMATH Open document ID: 0659.90099
DOI: 10.1007/BF01242864
author: S. H. Smith
published in: International Journal of Game Theory
publication date: 1988-01-01T00:00:00Z
review text: This paper considers a relationship between the modified strong equilibria of a repeated game and the modified \(\beta\)-core of the component game. Here the strong equilibrium concept is modified so that whenever a coalition S deviates from a given strategy n-tuple \(\bar s=(\bar s_ 1,...,\bar s_ n)\), the strategies \(\bar s_{N-S}\) of the complementary coalition N-S should be the best response for the new strategies of the deviating coalition S. The \(\beta\)-core is modified in the same manner. Then, instead of Aumann's theorem that the strong equilibria of a repeated game coincide with the \(\beta\)-core of the component game, it is obtained that the modified strong equilibria are included in the modified \(\beta\)-core of the component game. This is the main result of this papers.
reviewed by: Mamoru Kaneko
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 4079199
zbMATH Keywords: modified strong equilibria
zbMATH Keywords: repeated game
zbMATH Keywords: modified \(\beta\)-core
zbMATH Keywords: component game
MaRDI profile type: Publication
cites work: Strong perfect equilibrium in supergames
cites work: Cores in noncooperative games
description: scientific article; zbMATH DE number 4079199