Information Geometry and Evolutionary Game Theory

TL;DR

This paper explores the connection between information geometry and evolutionary game theory by representing the Shahshahani geometry as the Fisher information metric on the probability simplex, extending to complex systems.

Contribution

It introduces an information-theoretic framework for evolutionary game theory, linking geometric concepts with probability distributions and extending results to multi-population models.

Findings

Shahshahani geometry is realized as Fisher information metric.

Key concepts in evolutionary game theory are interpreted information-theoretically.

Extensions to Lotka-Volterra equations and multi-population systems are demonstrated.

Abstract

The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.