On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization

Lei Qiao, Haomiao Yu and Zhixiang Zhang

Games and Economic Behavior, 2016, vol. 99, issue C, 89-98

Abstract: We show that if every large game with a given player space and any given uncountable trait space (or action set) is a proper idealized limit, then the player space must be saturated. When the player space is allowed to be an arbitrary atomless probability space, even a non-saturated one such as the classical Lebesgue unit interval, we establish the following: (i) If a large game has a countable action set and a countable trait space, then the game has a closed Nash equilibrium correspondence, and is thus proper as an idealized limit; (ii) If every large game having a given action set and a given trait space is proper as an idealized limit, then both the action set and the trait space must be countable.

Keywords: Closed-graph property; Large game with traits (LGT); Lebesgue unit interval; Nash equilibrium; Nash equilibrium distribution; Saturated probability space (search for similar items in EconPapers)
JEL-codes: C65 C72 D84 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:99:y:2016:i:c:p:89-98

DOI: 10.1016/j.geb.2016.07.007

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