Intrinsic noise in game dynamical learning

TL;DR

This paper explores how intrinsic sampling noise in game learning models causes stochastic fluctuations that can sustain cycles or alter dynamics, contrasting with deterministic replicator equations.

Contribution

It introduces a stochastic model of game learning based on finite sampling, deriving analytical descriptions of noise effects on dynamics.

Findings

Finite sampling induces stochastic fluctuations in game learning.

Noise can sustain cycles or eliminate periodic orbits.

Analytical methods from statistical physics describe these fluctuations.

Abstract

Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations. We here show that similar noise-sustained trajectories arise in game dynamical learning, where the stochasticity has a different origin: agents sample a finite number of moves of their opponents in-between adaptation events. The limit of infinite batches results in deterministic modified replicator equations, whereas finite sampling leads to a stochastic dynamics. The characteristics of these fluctuations can be computed analytically using methods from statistical physics, and such noise can affect the attractors significantly, leading to noise-sustained cycling or removing periodic orbits of the standard replicator dynamics.