Satoh, Atsuhiro and Tanaka, Yasuhito (2018): The equivalence of minimax theorem and existence of Nash equilibrium in asymmetric threeplayers zerosum game with two groups.
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Abstract
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric threeplayers zerosum game with two groups. Two players are in Group A, and they have the same payoff function and strategy space. One player, Player C, is in Group C. Then,
1. The existence of a Nash equilibrium, which is symmetric in Group A, implies Sion's minimax theorem for pairs of a player in Group A and Player C with symmetry in Group A.
2. Sion's minimax theorem for pairs of a player in Group A and Player C with symmetry in Group A implies the existence of a Nash equilibrium which is symmetric in Group A.
Thus, they are equivalent.
Item Type:  MPRA Paper 

Original Title:  The equivalence of minimax theorem and existence of Nash equilibrium in asymmetric threeplayers zerosum game with two groups 
Language:  English 
Keywords:  threeplayers zerosum game, two groups, Nash equilibrium, Sion's minimax theorem 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  87249 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  16 Jun 2018 10:34 
Last Modified:  10 Oct 2019 20:33 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/87249 
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