Minimax theorem and Nash equilibrium of symmetric multi-players zero-sum game with two strategic variables

Masahiko Hattori; Atsuhiro Satoh; Yasuhito Tanaka

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arXiv · 1806.07203

Minimax theorem and Nash equilibrium of symmetric multi-players zero-sum game with two strategic variables

Masahiko Hattori·Atsuhiro Satoh·Yasuhito Tanaka

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Abstract

We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by invertible functions. Using the minimax theorem by \cite{sion} we will show that Nash equilibria in the following states are equivalent. 1. All players choose $t_i,\ i\in \{1, \dots, n\}$, (as their strategic variables). 2. Some players choose $t_i$'s and the other players choose $s_i$'s. 3. All players choose $s_i,\ i\in \{1, \dots, n\}$.

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Masahiko Hattori, Atsuhiro Satoh, Yasuhito Tanaka. 2018-06-17. Minimax theorem and Nash equilibrium of symmetric multi-players zero-sum game with two strategic variables. https://arxiv.org/abs/1806.07203

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