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On sustainable equilibria

Srihari Govindan, Rida Laraki and Lucas Pahl

Journal of Economic Theory, 2023, vol. 213, issue C

Abstract: Following the ideas laid out in Myerson (1996), Hofbauer (2003) defined a Nash equilibrium of a finite game as sustainable if it can be made the unique Nash equilibrium of a game obtained by deleting/adding a subset of the strategies that are inferior replies to it. This paper proves a result about sustainable equilibria and uses it to provide a refinement as well. Our result concerns the Hofbauer-Myerson conjecture about the relationship between the sustainability of an equilibrium and its index: for a generic class of games, an equilibrium is sustainable iff its index is +1. von Schemde and von Stengel (2008) proved this conjecture for bimatrix games; we show that the conjecture is true for all finite games. More precisely, we prove that an equilibrium is isolated and has index +1 if and only if it can be made unique in a larger game obtained by adding finitely many strategies that are inferior replies to that equilibrium. It follows in a straightforward way from our result that sustainable equilibria fail the Decomposition Axiom for games as formulated by Mertens (1989a). In order to rectify this problem we propose a refinement, called strongly sustainable equilibria, which is shown to exist for all regular games.

Keywords: Sustainable equilibria; Index of equilibria; Refinements of equilibria (search for similar items in EconPapers)
JEL-codes: C02 C72 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Working Paper: On sustainable equilibria (2023)
Working Paper: On Sustainable Equilibria (2021) Downloads
Working Paper: On Sustainable Equilibria (2020)
Working Paper: On Sustainable Equilibria (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:213:y:2023:i:c:s0022053123001321

DOI: 10.1016/j.jet.2023.105736

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