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Title: Reinforcement Nash Equilibrium Solver
Nash Equilibrium (NE) is the canonical solution concept of game theory, which provides an elegant tool to understand the rationalities. Though mixed strategy NE exists in any game with finite players and actions, computing NE in two- or multi-player general-sum games is PPAD-Complete. Various alternative solutions, e.g., Correlated Equilibrium (CE), and learning methods, e.g., fictitious play (FP), are proposed to approximate NE. For convenience, we call these methods as ``inexact solvers'', or ``solvers'' for short. However, the alternative solutions differ from NE and the learning methods generally fail to converge to NE. 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 alpha-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., alpha-rank, CE, FP and PRD, and can be generalized to unseen games.  more » « less
Award ID(s):
2414554 2302999
PAR ID:
10632699
Author(s) / Creator(s):
; ; ; ; ; ;
Publisher / Repository:
International Joint Conferences on Artificial Intelligence Organization
Date Published:
ISBN:
978-1-956792-04-1
Page Range / eLocation ID:
265 to 273
Format(s):
Medium: X
Location:
Jeju, South Korea
Sponsoring Org:
National Science Foundation
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