A General Framework for Optimizing and Learning Nash Equilibrium

TL;DR

This paper introduces a neural network-based framework for optimizing and learning Nash equilibria by estimating players' cost functions, applicable with different data availability scenarios.

Contribution

It proposes a general neural network framework with two approaches for Nash equilibrium learning, incorporating equilibrium constraints and validated through experiments.

Findings

Effective neural network models for cost function estimation.

Successful application of the framework in numerical experiments.

Versatile approaches for different data scenarios.

Abstract

One key in real-life Nash equilibrium applications is to calibrate players' cost functions. To leverage the approximation ability of neural networks, we proposed a general framework for optimizing and learning Nash equilibrium using neural networks to estimate players' cost functions. Depending on the availability of data, we propose two approaches (a) the two-stage approach: we need the data pair of players' strategy and relevant function value to first learn the players' cost functions by monotonic neural networks or graph neural networks, and then solve the Nash equilibrium with the learned neural networks; (b) the joint approach: we use the data of partial true observation of the equilibrium and contextual information (e.g., weather) to optimize and learn Nash equilibrium simultaneously. The problem is formulated as an optimization problem with equilibrium constraints and solved using a modified Backpropagation Algorithm. The proposed methods are validated in numerical experiments.