On Sustainable Equilibria
Srihari Govindan, Rida Laraki and Lucas Pahl, UNSW
Abstract: Following the ideas laid out in Myerson, Hofbauer 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 generic games, an equilibrium is sustainable iff its index is +1. von Schemde and von Stengel proved this conjecture for bimatrix games. This paper shows that the conjecture is true for all finite games.