On sustainable equilibria

Srihari Govindan, Rida Laraki () and Lucas Pahl
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Rida Laraki: LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, University of Liverpool, UM6P - Université Mohammed VI Polytechnique = Mohammed VI Polytechnic University [Ben Guerir]
Lucas Pahl: Universität Bonn = University of Bonn

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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)
Date: 2023-10
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Citations: View citations in EconPapers (1)

Published in Journal of Economic Theory, 2023, 213, pp.105736. ⟨10.1016/j.jet.2023.105736⟩

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Related works:
Journal Article: On sustainable equilibria (2023)
Working Paper: On Sustainable Equilibria (2021)
Working Paper: On Sustainable Equilibria (2020)
Working Paper: On Sustainable Equilibria (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04305157

DOI: 10.1016/j.jet.2023.105736

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