Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces. (English) Zbl 1319.91025
Summary: 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.
Keywords:
infinite-dimensional action space; nonatomic game; pure-strategy Nash equilibrium; saturated probability spaceReferences:
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