On Equilibrium in Pure Strategies in Games with Many Players

Arbeitspapier

Motivated by issues of imitation, learning and evolution, we introduce a framework of non-co-operative games, allowing both countable sets of pure actions and player types and player types and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash e-equilibrium in pure strategies that is 'e-equivalent'. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions and any other attributes that are not directly relevant to other players). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. We stress that for studying issues such as conformity, the case of a finite set of types and actions, while illuminating, cannot yield completely satisfactory results. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Nota di Lavoro ; No. 122.2003

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games
• Subject: Equilibrium ; Pure Strategies ; Non-cooperative Games ; Nash-Gleichgewicht ; Nichtkooperatives Spiel ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Cartwright, Edward ; Wooders, Myrna
• Event: Veröffentlichung
• (who): Fondazione Eni Enrico Mattei (FEEM)
• (where): Milano
• (when): 2003

Further information

• Handle: http://hdl.handle.net/10419/118148
• Last update: 10.03.2025, 11:44 AM CET