Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces
- First Online:
- Cite this article as:
- Sun, X. & Zhang, Y. Econ Theory (2015) 58: 161. doi:10.1007/s00199-013-0795-6
- 344 Downloads
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.