On Sustainable Equilibria - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

On Sustainable Equilibria

Srihari Govindan
  • Fonction : Auteur
Lucas Pahl
  • Fonction : Auteur
Felipe Garrido-Lucero
  • Fonction : Auteur
Andrew Jennings
  • Fonction : Auteur
Clemens Puppe
  • Fonction : Auteur
Estelle Varloot
  • Fonction : Auteur
Saeed Hadikhanloo
  • Fonction : Auteur
Panayotis Mertikopoulos
  • Fonction : Auteur
Sylvain Sorin
  • Fonction : Auteur

Résumé

Following the ideas laid out in Myerson (1996), Hofbauer (2000) 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 two results about sustainable equilibria. The first 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 isolated equilibrium 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. Our second result gives an axiomatic extension of sustainability to all games and shows that only the Nash components with positive index can be sustainable.

Dates et versions

hal-03451057 , version 1 (26-11-2021)

Identifiants

Citer

Srihari Govindan, Rida Laraki, Lucas Pahl, Felipe Garrido-Lucero, Andrew Jennings, et al.. On Sustainable Equilibria. 2021. ⟨hal-03451057⟩
35 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More