Deep Learning Across Games

TL;DR

This paper demonstrates that two neural networks trained adversarially on static bimatrix games can learn to approximate Nash equilibria, including risk-dominant solutions, across diverse game scenarios.

Contribution

It introduces a novel adversarial training method for neural networks to learn equilibrium strategies in static games, showing robustness and generalization.

Findings

Networks approximate Nash equilibria in all tested games.

In 2x2 games with multiple equilibria, networks select the risk-dominant equilibrium.

The learned strategies generalize to out-of-distribution games.

Abstract

We train two neural networks adversarially to play static games. At each iteration, a row and column network observe a new random bimatrix game and output individual mixed strategies. The parameters of each network are independently updated via stochastic gradient descent on a loss defined by the individual squared regret experienced in the game. Simulations show the joint behavior of the trained networks approximates a Nash equilibrium in all games. In $2\times2$ games with multiple equilibria, the networks select the risk dominant equilibrium. These findings, which are robust and generalise out-of-distribution, illustrate how equilibrium emerges from learning across heterogeneous games.