Reduced games, consistency, and the core

Reduced games, consistency, and the core

Journal	International Journal of Game Theory
Publisher	Physica Verlag, An Imprint of Springer-Verlag GmbH
ISSN	0020-7276 (Print) 1432-1270 (Online)
Issue	Volume 20, Number 4 / December, 1992
DOI	10.1007/BF01271129
Pages	325-334

K. Tadenuma¹

(1)	Department of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, 186 Tokyo, Japan

Received: 15 October 1990 Revised: 15 October 1991

Abstract This paper establishes an axiomatization of the core by means of an internal consistency property with respect to a new reduced game introduced by Moulin (1985). Given a payoff vector chosen by a solution for some game, and given a subgroup of agents, we define thereduced game as that in which each coalition in the subgroup could attain payoffs to its members only if they are compatible with the initial payoffs toall the members outside of the subgroup. The solution isconsistent if it selects the same payoff distribution for the reduced game as initially. We show that consistency together with individual rationality characterizes the core of both transferable and non-transferable utility games.

The author would be grateful to William Thomson, Hervé Moulin and a referee for helpful comments on earlier versions of this paper. Financial support of the Seimeikai is also gratefully acknowledged.