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On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games

Abstract : This paper studies the existence of some known equilibrium solution concepts in a large class of economic models with discontinuous payo functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition [34], and its recent improvements [3, 25, 35, 36]. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of an approximate equilibrium and of a sharing rule solution in pure and mixed strategies (Simon and Zame [38]). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that in any general equilibrium model with discontinuous preferences, there is a sharing rule solution.
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https://hal.archives-ouvertes.fr/hal-01071678
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Submitted on : Monday, October 6, 2014 - 2:45:08 PM
Last modification on : Friday, April 29, 2022 - 10:13:02 AM
Long-term archiving on: : Friday, April 14, 2017 - 2:00:38 PM

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  • HAL Id : hal-01071678, version 1

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Philippe Bich, Rida Laraki. On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games. 2014. ⟨hal-01071678⟩

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