Symmetry, Equilibria, and Approximate Equilibria in Games With Countably Many Players
Speaker
Shiran Rachmilevitch
Date
08/01/2014 - 12:00 - 10:00Add To Calendar
2014-01-08 10:00:00
2014-01-08 12:00:00
Symmetry, Equilibria, and Approximate Equilibria in Games With Countably Many Players
Abstract: I consider games with finite pure-strategy sets and countably many players. I present a “simple” example of such a game for which an ϵ-equilibrium exists for all ϵ > 0, but for which a Nash equilibrium does not exist. This game is not symmetric, which is inevitable in the following sense: under a mild condition on the utility function – the co-finiteness condition – existence of an ϵ-equilibrium for all ϵ > 0 in a symmetric game implies the existence of a Nash equilibrium in that game. The co-finiteness condition is logically unrelated to continuity.
Keywords: ϵ equilibrium, equilibrium non-existence, innite games, symmetry, tail events.
JEL Codes: C72.
אוניברסיטת בר-אילן - Department of Economics
Economics.Dept@mail.biu.ac.il
Asia/Jerusalem
public
Affiliation
Haifa University
Abstract
Abstract: I consider games with finite pure-strategy sets and countably many players. I present a “simple” example of such a game for which an ϵ-equilibrium exists for all ϵ > 0, but for which a Nash equilibrium does not exist. This game is not symmetric, which is inevitable in the following sense: under a mild condition on the utility function – the co-finiteness condition – existence of an ϵ-equilibrium for all ϵ > 0 in a symmetric game implies the existence of a Nash equilibrium in that game. The co-finiteness condition is logically unrelated to continuity.
Keywords: ϵ equilibrium, equilibrium non-existence, innite games, symmetry, tail events.
JEL Codes: C72.
Attached file
Last Updated Date : 17/12/2013