Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form

Qilong Liu () and Qingshui Liao
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Qilong Liu: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
Qingshui Liao: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Mathematics, 2023, vol. 11, issue 10, 1-17

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.

Keywords: k -mode symmetric tensor; tensor complementary problem; m -person game; symmetric Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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