Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5071521 | Games and Economic Behavior | 2016 | 10 Pages |
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.
Related Topics
Social Sciences and Humanities
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Economics and Econometrics
Authors
Lei Qiao, Haomiao Yu, Zhixiang Zhang,