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

Xiang Sun and Yongchao Zhang ()

Economic Theory, 2015, vol. 58, issue 1, 182 pages

Abstract: 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. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Infinite-dimensional action space; Nonatomic game; Pure-strategy Nash equilibrium; Saturated probability space; C62; C72 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00199-013-0795-6

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