Equilibria existence in regular discontinuous games

Arbeitspapier

Many conditions have been introduced to weaken the continuity re-quirements for equilibrium existence in games. We introduce a new con-dition, called regularity, that is simple and easy to verify. It is implied both by Reny's better-reply security and Simon and Zame's endogenous sharing rule method. Regularity implies that the limits of €-equilibria are equilibria. Since this condition is weak, it is yet not enough to ensure pure strategy equilibrium existence, but we are able to identify extra conditions that, together with regularity, are sufficient for equilibrium existence. One is the marginal continuity property introduced by Prokopovych (2008), while the second is the well behavior of a sequence of approximating con-tinuous functions. In this way, we provide new equilibrium existence re-sults for discontinuous games under conditions that are simpler and easier to check than most of the available alternatives.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper ; No. 1463

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
• Subject: discontinuous games ; weak payoff security ; better-reply security ; regularity ; regular games ; epsilon-equilibria ; approximating sequence ; Nash-Gleichgewicht ; Nichtkooperatives Spiel ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): de Castro, Luciano I.
• Event: Veröffentlichung
• (who): Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science
• (where): Evanston, IL
• (when): 2008

Further information

• Handle: http://hdl.handle.net/10419/59627
• Last update: 10.03.2025, 11:42 AM CET