Reinforcement Nash Equilibrium Solver

Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Computing NE in two-or multi-player general-sum games is PPAD-Complete. Therefore, in this work, we propose REinforcement Nash Equilibrium Solver (RENES), which trains a single policy to modify the games with different sizes and applies the solvers on the modified games where the obtained solution is evaluated on the original games. Specifically, our contributions are threefold. i) We represent the games as 𝛼-rank response graphs and leverage graph neural network (GNN) to handle the games with different sizes as inputs; ii) We use tensor decomposition, e.g., canonical polyadic (CP), to make the dimension of modifying actions fixed for games with different sizes; iii) We train the modifying strategy for games with the widely-used proximal policy optimization (PPO) and apply the solvers to solve the modified games, where the obtained solution is evaluated on original games. Extensive experiments on large-scale normal-form games show that our method can further improve the approximation of NE of different solvers, i.e., 𝛼-rank, CE, FP and PRD, and can be generalized to unseen games.