Time Complexity Analysis of an Evolutionary Algorithm for approximating Nash Equilibriums

TL;DR

This paper analyzes the asymptotic time complexity of an approximation algorithm for Nash equilibria, showing that for 2x2 games the worst-case complexity is linear in the number of actions, with empirical validation on classic games.

Contribution

It provides the first asymptotic time complexity analysis of an evolutionary algorithm for approximating Nash equilibria, especially for 2x2 games.

Findings

Worst-case complexity is linear in the number of actions for 2x2 games

Empirical validation on Prisoner's Dilemma, Stag Hunt, Battle, and Chicken

Framework's potential applicability to other PPAD problems

Abstract

The framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$ problems. The correctness of this framework has been empirically validated on 4 well-studied 2x2 games: Prisoner's Dilemma, Stag Hunt, Battle, and Chicken. In this paper, we provide the asymptotic time-complexities for these methods and in particular, verify that for 2x2 games the worst-case complexity is linear in the number of actions an agent can choose from.