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Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form

Author

Listed:
  • Qilong Liu

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

  • Qingshui Liao

    (School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)

Abstract

In an m -person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player k in an m -person symmetric game is k -mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the m -person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

Suggested Citation

  • Qilong Liu & Qingshui Liao, 2023. "Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form," Mathematics, MDPI, vol. 11(10), pages 1-17, May.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2268-:d:1145613
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    References listed on IDEAS

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