Skip to main content

The same material has been published in Mathematical Social Sciences 6 (1983), 27-48, the only definitive repository of the content that has been certified and accepted after peer review.

Copyright and all rights therein are retained by North Holland. This material may not be copied or reposted without explicit permission. (Copyright (C) 1983 by North Holland, Inc.). North Holland is on the web at

Approximate Cores of Replica Games and Economies: Part 1: Replica games, externalities and approximate cores

Martin Shubik
Cowles Foundation for Research in Economics, Yale Univeristy
Myrna Holtz Wooders
Department of Economics, University of Toronto,

Received 1 August 1983

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 fare 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 where the 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