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Rank Reduction in Bimatrix Games

Author

Listed:
  • 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)

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.

Suggested Citation

  • Joseph L. Heyman & Abhishek Gupta, 2023. "Rank Reduction in Bimatrix Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 25(01), pages 1-29, March.
    • Handle: RePEc:wsi:igtrxx:v:25:y:2023:i:01:n:s0219198922500177
    DOI: 10.1142/S0219198922500177
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    Citations

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    Cited by:

    1. M. Ali Khan & Arthur Paul Pedersen & David Schrittesser, 2024. "Two-Person adversarial games are zero-sum: A resolution of the Luce-Raiffa-Aumann (LRA) conjecture," Papers 2403.04029, arXiv.org, revised Mar 2024.

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