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

Listed author(s):
  • Qiao, Lei
  • Yu, Haomiao
  • Zhang, Zhixiang

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 99 (2016)
Issue (Month): C ()
Pages: 89-98

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Handle: RePEc:eee:gamebe:v:99:y:2016:i:c:p:89-98
DOI: 10.1016/j.geb.2016.07.007
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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