Nash Equilibria via Stochastic Eigendecomposition

TL;DR

This paper introduces a new approach to approximate Nash equilibria in finite games using stochastic eigendecomposition techniques, bridging game theory and machine learning with practical linear algebra algorithms.

Contribution

It presents a novel reformulation of Nash equilibrium computation as solving parameterized polynomial systems using stochastic linear algebra methods.

Findings

Able to approximate all equilibria of general-sum games

Uses only stochastic SVD and power iteration algorithms

Demonstrates biological plausibility of the approach

Abstract

This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable complexity. In doing so, it forges an itinerant loop from game theory to machine learning and back. We show a Nash equilibrium can be approximated with purely calls to stochastic, iterative variants of singular value decomposition and power iteration, with implications for biological plausibility. We provide pseudocode and experiments demonstrating solving for all equilibria of a general-sum game using only these readily available linear algebra tools.