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Essentially the same material has been published in Mathematical Social Sciences 12 (1986), 105-137, the only definitive repository of the content that has been certified and accepted after peer review. The version of the paper here has some additional footnotes inserted; these are clearly noted as additions. At this time, the figures are missing. Also, this version may have some typographical errors not found in the published version; hopefully, they will eventually all be corrected. Copyright and all rights therein are retained by North Holland. This material may not be copied or reposted without explicit permission. (Copyright (C)1986 by North Holland, Inc.). North Holland is on the web at

The core of a game with a continuum of players and finite coalitions; The model and some results

Mamoru Kaneko; Department of Economics, Hitotsubashi University, Kunitachi, Tokyo 186, Japan
Myrna Holtz Wooders; Department of Economics, University of Toronto, Toronto, Ontario, Canada

Communicated by K.H. Kim

Received 1 August 1985

Revised 22, October 1985.

In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions -- ones containing only finite numbers of players -- are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions.This is appropriate in view of our restrictions on coalition formation. Once feasible outcomes are properly defined, the core concept is standard -- no permissible coalition can improve upon its outcome. We provide a sufficient condition for the nonemptiness of the core in the case wherethe players can be divided into a finite number of types. This result is applied to a market game and the nonemptiness of the core of the market game is stated under considerably weaker conditions (but with finite types). In addition, it is illustrated that the framework applies to assignment games with a continuum of players.

Key words continuum of players; finite coalitions; measure-consistent partitions; game in characteristic function form; f-core.

Mathematical Social Sciences 12 (1986)Copyright© 1986 North Holland