Rank Reduction in Bimatrix Games

Joseph L. Heyman and Abhishek Gupta ()
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Joseph L. Heyman: Electrical Engineering and Computer Science, United States Military Academy, 606 Thayer Rd, West Point, New York 10996, USA
Abhishek Gupta: ��Electrical and Computer Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210, United State

International Game Theory Review (IGTR), 2023, vol. 25, issue 01, 1-29

Abstract: 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.

Keywords: Bimatrix games; Wedderburn rank reduction; matrix pencils; strategic equivalence in games (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219198922500177

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