Satoh, Atsuhiro and Tanaka, Yasuhito (2018): Sion's minimax theorem and Nash equilibrium in a multiplayers game with two groups which is zerosum and symmetric in each group.

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Abstract
We consider the relation between Sion's minimax theorem for a continuous function and Nash equilibrium in a multiplayers game with two groups which is zerosum and symmetric in each group. We will show the following results.
1. The existence of Nash equilibrium which is symmetric in each group implies a modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy for players in each group. %given the values of the strategic variables.
2. A modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy for players in each group implies the existence of Nash equilibrium which is symmetric in each group.
Thus, they are equivalent. An example of such a game is a relative profit maximization game in each group under oligopoly with two groups such that firms in each group have the same cost functions and maximize their relative profits in each group, and the demand functions are symmetric for the firms in each group.
Item Type:  MPRA Paper 

Original Title:  Sion's minimax theorem and Nash equilibrium in a multiplayers game with two groups which is zerosum and symmetric in each group 
Language:  English 
Keywords:  multiplayers 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:  88977 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  15 Sep 2018 07:20 
Last Modified:  02 Oct 2019 01:05 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/88977 