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The single deviation property in games with discontinuous payoffs

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Abstract

We study equilibrium existence in normal form games in which it is possible to associate with each nonequilibrium point an open neighborhood, a set of players, and a collection of deviation strategies, such that at any nonequilibrium point of the neighborhood, a player from the set can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established as an application of a general equilibrium existence result for qualitative games. A new form of the better-reply security condition, called the strong single deviation property, is proposed.

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Authors and Affiliations

  1. Kyiv School of Economics and Kyiv Economics Institute, 13 Yakira, Office 327, Kyiv, 04119, Ukraine

    Pavlo Prokopovych

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  1. Pavlo Prokopovych
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Correspondence to Pavlo Prokopovych.

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This paper supersedes the earlier 2010 version of the paper circulated under the title “Domain L-Majorization and Equilibrium Existence in Discontinuous Games.” I am grateful to Roy Gardner, Yuriy Gorodnichenko, Idione Soza, Nicholas Yannelis, and anonymous referees for helpful discussions, comments, and suggestions.

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Prokopovych, P. The single deviation property in games with discontinuous payoffs. Econ Theory 53, 383–402 (2013). https://doi.org/10.1007/s00199-012-0696-0

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  • DOI: https://doi.org/10.1007/s00199-012-0696-0

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