SFB 303 Discussion Paper No. B - 149

Author: Winter, Eyal, and Myrna Holtz Wooders
Title: An Axiomatization of the Core for Finite and Continuum Games
Abstract: In this paper, we provide an axiomatization of the core of a game, where the class of games considered includes both finite games and continuum games with finite coalitions. Our axiomatization extends those of Peleg (1985, 1986), to the class of continuum games introduced by Kaneko-Wooders (1985, 1986a), and further studied and applied to large economies in Hammond-Kaneko-Wooders (1989) and Kaneko-Wooders (1989).The invariance of our axiomatization between finite and continuum games reflects the invariance of the concept of the player between both models of games. In a finite model, no matter how large the total player sets, two players can form a coalition. In contrast, in the continuum model of Dubey-Neyman (1984) with only coalitions containing nonnegligible percentages of the total player sets, two players (or indeed, any finite number of players) are completely ineffectual.
Creation-Date: June 1990
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