Hattori, Masahiko and Satoh, Atsuhiro and Tanaka, Yasuhito (2018): Minimax theorem and Nash equilibrium of symmetric threeplayers zerosum game with two strategic variables.

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Abstract
We consider a symmetric threeplayers zerosum game with two strategic variables. Three players are Players A, B and C. Two strategic variables are ti and si, i = A;B;C. They are related by invertible functions. Using the minimax theorem by Sion (1958) and the fixed point theorem by Glicksberg (1952) we will show that Nash equilibria in the following four states are equivalent. 1. All players, Players A, B and C choose ti; i = A;B;C, (as their strategic variables). 2. Two players choose ti's, and one player chooses si. 3. One player chooses ti, and two players choose si's. 4. All players, Players A, B and C choose si; i = A;B;C.
Item Type:  MPRA Paper 

Original Title:  Minimax theorem and Nash equilibrium of symmetric threeplayers zerosum game with two strategic variables 
Language:  English 
Keywords:  symmetric threeperson zerosum game, Nash equilibrium, two strategic variables 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  85503 
Depositing User:  Mr Atsuhiro Satoh 
Date Deposited:  28 Mar 2018 19:10 
Last Modified:  03 Oct 2019 16:26 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/85503 