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Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form
Version 1
: Received: 24 April 2023 / Approved: 24 April 2023 / Online: 24 April 2023 (09:40:34 CEST)
A peer-reviewed article of this Preprint also exists.
Liu, Q.; Liao, Q. Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form. Mathematics 2023, 11, 2268. Liu, Q.; Liao, Q. Computing Nash Equilibria for Multiplayer Symmetric Games Based on Tensor Form. Mathematics 2023, 11, 2268.
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
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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