Neural Algorithmic Reasoning for Nash Equilibrium

Mateusz Kuba Korytkowski, Dobrik Georgiev Georgiev, Davide Buffelli, Pietro Lio

Keywords: Nash Equilibrium, Neural Algorithmic Reasoning, Game Theory

Abstract: We apply Neural Algorithmic Reasoning (NAR) to Nash Equilibrium computation in two-player zero-sum games. We represent bimatrix games as bipartite graphs and train a GNN processor to imitate Fictitious Play. The resulting model, NAR-FP, combines GATv2 attention with GRU memory and per-step trajectory supervision. Using the multi-size training protocol, NAR-FP achieves strong out-of-distribution size generalisation, with only $1.02\times$ exploitability degradation from $10{\times}10$ to $50{\times}50$ games. NAR-FP outperforms classical Fictitious Play at matched step budgets, learning to accelerate the algorithm rather than merely replicate it. It also generalises across game structures, outperforming FP on cyclic games never seen during training. Our results suggest that algorithmic alignment is an effective framework for bridging classical game-theoretic solvers and modern neural learning.

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Paper Type: Short paper

Submission Number: 11