The Replicator Equation as an Inference Dynamic

TL;DR

This paper interprets the replicator equation as a continuous inference process, linking evolutionary dynamics with Bayesian inference, and explores connections involving information geometry and exponential families.

Contribution

It introduces a novel interpretation of the replicator equation as an inference dynamic, bridging evolutionary game theory and Bayesian inference.

Findings

Replicator equation can be viewed as a continuous inference process.

Connections between information divergences and replicator dynamics are established.

Exponential families are identified as solutions within the replicator dynamic framework.

Abstract

The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator equation are given including a discussion of information divergences and exponential families as solutions for the replicator dynamic, using Fisher information and information geometry.