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Continuum and Finite-Player Noncooperative Models of Competition

Green, Edward J. (1982) Continuum and Finite-Player Noncooperative Models of Competition. Social Science Working Paper, 418. California Institute of Technology , Pasadena, CA. (Unpublished)

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The anonymous interaction of large numbers of economic agents is a kind of noncooperative situation which is markedly different from small-numbers strategic conflict. The mathematical model of a nonatomic game, or a game with a continuum of players, has been introduced as a model for these many-agent situations on the basis that its equilibria should closely approximate those of games with large finite numbers of players. This paper contains a precise definition of what it means for a nonatomic game to be the limit of a sequence of finite-player games, and a theorem which states when the limit of equilibria of finite-player games will be an equilibrium of the nonatomic limit game. This is analogous to theorems prompted by Edgeworth's conjecture in core theory. It is derived from a general set of sufficient conditions for the graph of a noncooperative equilibrium correspondence to be closed.

Item Type:Report or Paper (Working Paper)
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Additional Information:I would like to thank Marcus Berliant, Donald Brown, Tatsuro Ichiishi, Ariel Rubenstein and Hugo Sonnenschein for their thoughtful comments on early drafts of this paper. Published as Green, Edward J. "Continuum and finite-player noncooperative models of competition." Econometrica: Journal of the Econometric Society (1984): 975-993.
Group:Social Science Working Papers
Subject Keywords:Mathematical vectors, Topology, Economic theory, Game theory, Topological spaces, Topological theorems, Statistical theories, Mathematical functions, Economic models, Mathematical theorems
Series Name:Social Science Working Paper
Issue or Number:418
Record Number:CaltechAUTHORS:20171003-151303475
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82011
Deposited By: Jacquelyn Bussone
Deposited On:04 Oct 2017 19:04
Last Modified:03 Oct 2019 18:49

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