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A Study on Equitablity of a Matrix Game

IU Depautment

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Abstract

It is common knowledge that a zero sum two-person finite game is also called matrix game. Suppose two players who play a matrix game hope that the game result is as equitable as possible. A game solution is called optimal if the game result is most equitable when two players use the strategies in the game solution. In this paper, we prove some properties of a set of optimal game solutions. And we also give the concept of equitable degree of a matrix game and prove some interesting results about it.

About this research paper

What this paper is about

It is common knowledge that a zero sum two-person finite game is also called matrix game. Suppose two players who play a matrix game hope that the game result is as equitable as possible. A game solution is called optimal if the game result is most equitable when two players use the strategies in the game solution. In this paper, we prove some properties of a set of optimal game solutions. And we also give the concept of equitable degree of a matrix game and prove some interesting results about it.

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Available abstract

It is common knowledge that a zero sum two-person finite game is also called matrix game. Suppose two players who play a matrix game hope that the game result is as equitable as possible. A game solution is called optimal if the game result is most equitable when two players use the strategies in the game solution. In this paper, we prove some properties of a set of optimal game solutions. And we also give the concept of equitable degree of a matrix game and prove some interesting results about it.

Key concepts: Normal-form game, Repeated game, Sequential game, Example of a game without a value, Mathematical economics, Screening game, Simultaneous game, Matrix (chemical analysis)

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