2018•arXiv (Cornell University)Open access
On the relation between Sion's minimax theorem and existence of Nash\n equilibrium in asymmetric multi-players zero-sum game with only one alien
Atsuhiro Satoh, Yasuhito Tanaka
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Abstract
We consider the relation between Sion's minimax theorem for a continuous\nfunction and a Nash equilibrium in an asymmetric multi-players zero-sum game in\nwhich only one player is different from other players, and the game is\nsymmetric for the other players. Then,\n 1. The existence of a Nash equilibrium, which is symmetric for players other\nthan one player, implies Sion's minimax theorem for pairs of this player and\none of other players with symmetry for the other players.\n 2. Sion's minimax theorem for pairs of one player and one of other players\nwith symmetry for the other players implies the existence of a Nash equilibrium\nwhich is symmetric for the other players.\n Thus, they are equivalent.\n
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