Stability and largeness of core for symmetric games

Stability and largeness of core for symmetric games

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Article ID: iaor2001934
Country: Germany
Volume: 29
Issue: 1
Start Page Number: 11
End Page Number: 22
Publication Date: Jan 2000
Journal: International Journal of Game Theory
Authors: , ,
Abstract:

Largeness of the core is sufficient for stability of the core. In general the necessity is not known. In this paper we answer affirmatively the necessity for symmetric games. We also prove its equivalence to n specified vectors being imputations and also to the convexity of the lower boundary of the set of all acceptable pay-off vectors of the game. In this paper we establish the equivalence of a condition given by Shapley to the newly evolved condition, thereby give an alternate proof to Shapley's condition.

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