Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games

• URL: http://arxiv.org/abs/2509.25618v1
• Date: Tue, 30 Sep 2025 00:28:21 GMT
• Title: Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games
• Authors: Sam Ganzfried,
• Abstract summary: We present an approach to approximation in multiplayer imperfectinformation games that solves a quadratically-constrained program based on a nonlinear approximation.<n>We also lead to a new approach for computing Nash equilibrium in multiplayer strategic-form games.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have convergence guarantees in two-player zero-sum games, they do not guarantee convergence to Nash equilibrium in multiplayer games. We present an approach for exact computation of Nash equilibrium in multiplayer imperfect-information games that solves a quadratically-constrained program based on a nonlinear complementarity problem formulation from the sequence-form game representation. This approach capitalizes on recent advances for solving nonconvex quadratic programs. Our algorithm is able to quickly solve three-player Kuhn poker after removal of dominated actions. Of the available algorithms in the Gambit software suite, only the logit quantal response approach is successfully able to solve the game; however, the approach takes longer than our algorithm and also involves a degree of approximation. Our formulation also leads to a new approach for computing Nash equilibrium in multiplayer strategic-form games which we demonstrate to outperform a previous quadratically-constrained program formulation.

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