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Economic Theory

, Volume 48, Issue 1, pp 47–65

First Online: 21 October 2010Received: 17 September 2009Accepted: 03 October 2010


For games with discontinuous payoffs Simon and Zame Econometrica 58:861–872, 1990 introduced payoff indeterminacy, in the form of endogenous sharing rules, which are measurable selections of a certain payoff correspondence. Their main result concerns the existence of a mixed Nash equilibrium and an associated sharing rule. Its proof is based on a discrete approximation scheme -from within- the payoff correspondence. Here, we present a new, related closure result for games with possibly noncompact action spaces, involving a sequence of Nash equilibria. In contrast to Simon and Zame Econometrica 58:861–872, 1990, this result can be used for more involved forms of approximation, because it contains more information about the endogenous sharing rule. With such added precision, the closure result can be used for the actual computation of endogenous sharing rules in games with discontinuous payoffs by means of successive continuous interpolations in an approximation scheme. This is demonstrated for a Bertrand type duopoly game and for a location game already considered by Simon and Zame. Moreover, the main existence result of Simon and Zame Econometrica 58:861–872, 1990 follows in two different ways from the closure result.

KeywordsNash equilibrium Discontinuous games Weak convergence of probability measures Endogenous sharing rule Kuratowski limes superior A question by an anonymous referee helped and stimulated the author to demarcate the present paper’s position with respect to Simon and Zame 1990. Also, remarks by Guilherme Carmona helped to improve the presentation.

JEL ClassificationC72  Download to read the full article text

Autor: Erik J. Balder



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