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Two person zero-sum game with two sets of strategic variables

Satoh, Atsuhiro and Tanaka, Yasuhito (2016): Two person zero-sum game with two sets of strategic variables.

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Abstract

We consider a two-person zero-sum game with two sets of strategic variables which are related by invertible functions. They are denoted by (sA, sB) and (tA, tB) for players A and B.

We will show that the following four patterns of competition are equivalent, that is, they yield the same outcome.

1. Player A and B choose sA and sB (competition by (sA, sB)).

2. Player A and B choose tA and tB (competition by (tA, tB)).

3. Player A and B choose tA and sB (competition by (tA, sB)).

4. Player A and B choose sA and tB (competition by (sA, tB)).

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