On the relationship between imitative logit dynamics in the population game theory and mirror descent method in the online optimization using the example of the Shortest Path Problem

TL;DR

This paper explores the connection between imitative logit dynamics in population game theory and mirror descent in convex optimization, illustrating their relationship through the example of the Shortest Path Problem.

Contribution

It establishes a novel interpretation linking population game dynamics with optimization methods, specifically connecting imitative logit dynamics to mirror descent.

Findings

Demonstrates the equivalence of the two dynamics in the context of the Shortest Path Problem

Provides insights into the theoretical relationship between game theory and optimization methods

Suggests potential for cross-disciplinary applications and analysis

Abstract

In this paper we describe how imitative logit dynamic (rather popular in population games theory) can be interpreted in terms of mirror descent method (well known in convex optimization). We demonstrate the connection of this two type dynamics on the Shortest Path Problem.