Logit Equilibrium as an Approximation of Nash Equilibrium

TL;DR

This paper demonstrates that the logit equilibrium provides a smooth, uniform approximation to the Nash equilibrium manifold, offering a new perspective on equilibrium analysis in game theory.

Contribution

It establishes that the logit equilibrium correspondence forms a smooth manifold that approximates the Nash equilibrium manifold, bridging the gap between these concepts.

Findings

Logit equilibrium graph is a smooth manifold.

Logit equilibrium uniformly approximates Nash equilibrium.

Provides a geometric understanding of equilibrium approximation.

Abstract

We prove that the graph of the logit equilibrium correspondence is a smooth manifold, which uniformly approximates the graph of the Nash equilibrium manifold.