# Population Games and Discrete Optimal Transport

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## Abstract

We propose an evolutionary dynamics for population games with discrete strategy sets, inspired by optimal transport theory and mean field games. The proposed dynamics is the Smith dynamics with strategy graph structure, in which payoffs are modified by logarithmic terms. The dynamics can be described as a Fokker–Planck equation on a discrete strategy set. For potential games, the dynamics is a gradient flow system under a Riemannian metric from optimal transport theory. The stability of the dynamics is studied through optimal transport metric tensor, free energy and Fisher information.

## Keywords

Evolutionary game theory Optimal transport Mean field games Fokker–Planck equations## Notes

### Acknowledgements

This paper is based on Wuchen Li’s thesis Li (2016).

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