Economic Theory

, Volume 58, Issue 1, pp 161–182

Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces

Research Article

DOI: 10.1007/s00199-013-0795-6

Cite this article as:
Sun, X. & Zhang, Y. Econ Theory (2015) 58: 161. doi:10.1007/s00199-013-0795-6


This paper studies the existence of pure-strategy Nash equilibria for nonatomic games where players take actions in infinite-dimensional Banach spaces. For any infinite-dimensional Banach space, if the player space is modeled by the Lebesgue unit interval, we construct a nonatomic game which has no pure-strategy Nash equilibrium. But if the player space is modeled by a saturated probability space, there is a pure-strategy Nash equilibrium in every nonatomic game. Finally, if every game with a fixed nonatomic player space and a fixed infinite-dimensional action space has a pure-strategy Nash equilibrium, the underlying player space must be saturated.


Infinite-dimensional action space Nonatomic game  Pure-strategy Nash equilibrium Saturated probability space 

JEL Classification

C62 C72 

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Economics and Management SchoolWuhan UniversityWuhanChina
  2. 2.School of EconomicsShanghai University of Finance and EconomicsShanghaiChina
  3. 3.Key Laboratory of Mathematical Economics (SUFE)Ministry of EducationShanghaiChina

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