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Existence of pure strategy equilibria in Bertrand-Edgeworth games with imperfect divisibility of money

De Francesco, Massimo A. (2008): Existence of pure strategy equilibria in Bertrand-Edgeworth games with imperfect divisibility of money.

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Abstract

This paper incorporates imperfect divisibility of money in a price game where a given number of identical firms produce a homogeneous product at constant unit cost up to capacity. We find necessary and sufficient conditions for the existence of a pure strategy equilibrium. Unlike in the continuous action space case, under discrete pricing there may be a range of symmetric pure strategy equilibria - which we fully characterize - a range which may or may not include the competitive price. Also, we determine the maximum number of such equilibria when competitive pricing is itself an equilibrium.

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