Stochastic gain in population dynamics

TL;DR

This paper extends replicator dynamics with adaptive learning rates, demonstrating that populations can leverage noise and fluctuations to temporarily outperform equilibrium payoffs, akin to stochastic resonance, with potential applications in economics.

Contribution

It introduces a novel adaptive learning rate mechanism in population dynamics that exploits noise to enhance payoffs and system properties.

Findings

Populations with dynamic learning rates outperform static ones in transient phases.

External noise can be exploited to surpass Nash equilibrium payoffs.

The payoff versus noise curve exhibits stochastic resonance-like behavior.

Abstract

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a reasonance-like fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.