On Sustainable Equilibria

Govindan, Srihari, Laraki, Rida ORCID: 0000-0002-4898-2424 and Pahl, Lucas (2020) On Sustainable Equilibria. In: EC '20: The 21st ACM Conference on Economics and Computation.

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Abstract

Following the ideas laid out in Myerson (1996), Hofbauer (2000) defined an equilibrium of a game as sustainable if it can be made the unique equilibrium of a game obtained by deleting a subset of the strategies that are inferior replies to it, and then adding others. Hofbauer also formalized Myerson's 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. This paper shows that the conjecture is true for all finite games. More precisely, we prove that an isolated equilibrium of a given game has index +1 if and only if it can be made unique in a larger game obtained by adding finitely many inferior reply strategies.

Item Type:	Conference or Workshop Item (Unspecified)
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	12 Aug 2022 10:27
Last Modified:	18 Jan 2023 20:53
DOI:	10.1145/3391403.3399514
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3161055