# Nash Equilibrium Approximation under Communication and Computation Constraints in Large-Scale Non-cooperative Games

## TL;DR

This paper addresses the challenge of approximating Nash equilibria in large-scale mean-field games with communication and computation constraints, proposing methods that reduce costs while maintaining accuracy.

## Contribution

It introduces three novel approximation methods for the asymptotic equilibrium mean in constrained large-scale games, with theoretical analysis and numerical validation.

## Key findings

- Convergence of equilibrium mean variables to a constant as agents increase
- Proposed methods significantly reduce communication and computation costs
- Numerical examples demonstrate the accuracy of the approximation methods

## Abstract

This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility function of each agent depends on its action, the average of other agents' actions (called the mean variable of that agent) and a deterministic parameter. It is shown that the equilibrium mean variables of all agents converge uniformly to a constant, called asymptotic equilibrium mean (AEM), as the number of agents tends to infinity. The AEM, which depends on the limit of empirical distribution of agents' parameters, determines the asymptotic equilibrium behavior of agents. Next, the problem of approximating the AEM at a processing center under communication and computation constraints is studied. Three approximation methods are proposed to substantially reduce the communication and computation costs of approximating AEM at the processing center. The accuracy of the proposed approximation methods is analyzed and illustrated through numerical examples.