Stochastic Replicator Dynamics Subject to Markovian Switching

TL;DR

This paper studies stochastic replicator dynamics influenced by Markovian environmental changes, providing conditions for long-term behavior similar to deterministic models and extending analysis from two states to general finite states.

Contribution

It introduces a Markov chain-based model for environmental variability in stochastic replicator dynamics and characterizes long-run behavior under these stochastic influences.

Findings

Conditions for long-term behavior analogous to deterministic dynamics

Extension from two-state to general finite-state Markov chains

Analysis of stochastic effects on population strategy evolution

Abstract

Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is modeled by a continuous time Markov chain in a finite atom space. We establish conditions for this dynamic to have an analogous characterization of the long-run behavior to that of the deterministic dynamic. To create intuition, we first consider the case when the Markov chain has two states. A very natural extension to the general finite state space of the Markov chain will be given.