# Population games and Discrete optimal transport

## TL;DR

This paper introduces a novel evolutionary dynamic for population games with discrete strategies, inspired by optimal transport and mean field game theory, modeled as a gradient flow of free energy.

## Contribution

It develops a new discrete-time dynamic based on optimal transport principles, linking population game behavior to Markov processes and gradient flow structures.

## Key findings

- Dynamics are described by a Fokker-Planck equation on discrete strategies.
- Stability governed by optimal transport, entropy, and Fisher information.
- Models behavior of irrational, myopic, greedy players.

## Abstract

We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy set. The derived dynamics is the gradient flow of a free energy and the transition density equation of a Markov process. Such process provides models for the behavior of the individual players in population, which is myopic, greedy and irrational. The stability of the dynamics is governed by optimal transport metric, entropy and Fisher information.