Rank Reduction in Bimatrix Games

Joseph L. Heyman; Abhishek Gupta

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Rank Reduction in Bimatrix Games

机译：Rank Reduction in Bimatrix Games

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摘要

The rank of a bimatrix game is defined as the rank of the sum of the payoff matrices of the two players. The rank of a game is known to impact both the most suitable computation methods for determining a solution and the expressive power of the game. Under certain conditions on the payoff matrices, we devise a method that reduces the rank of the game without changing the equilibria of the game. We leverage matrix pencil theory and the Wedderburn rank reduction formula to arrive at our results. We also present a constructive proof of the fact that in a generic square game, the rank of the game can be reduced by 1, and in generic rectangular game, the rank of the game can be reduced by 2 under certain assumptions.

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《International game theory review》 |2023年第1期|1.1-1.29|共29页
作者
Joseph L. Heyman; Abhishek Gupta;
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作者单位

Electrical Engineering and Computer Science, United States Military Academy, 606 Thayer Rd, West Point, New York 10996,USA;

Electrical and Computer Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210,United State;

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原文格式 PDF
正文语种英语
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关键词
Bimatrix games; Wedderburn rank reduction; matrix pencils; strategic equivalence in games;

Rank Reduction in Bimatrix Games

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