The Kullback-Leibler Divergence as a Lyapunov Function for Incentive Based Game Dynamics

TL;DR

This paper extends the use of Kullback-Leibler divergence as a Lyapunov function to a broader class of incentive-based game dynamics, providing new conditions for stability of rest points.

Contribution

It generalizes the Lyapunov function approach from replicator equations to incentive dynamics, establishing broader stability criteria.

Findings

Kullback-Leibler divergence is a Lyapunov function for incentive dynamics.

Provides sufficient conditions for asymptotic stability of rest points.

Unifies previous results as special cases of the main theorem.

Abstract

It has been shown that the Kullback-Leibler divergence is a Lyapunov function for the replicator equations at evolutionary stable states, or ESS. In this paper we extend the result to a more general class of game dynamics. As a result, sufficient conditions can be given for the asymptotic stability of rest points for the entire class of incentive dynamics. The previous known results will be can be shown as corollaries to the main theorem.