The dynamics of competitive learning: the role of updates and memory

TL;DR

This paper investigates how memory and update methods influence competitive learning dynamics, revealing phase transitions, universality classes, and the impact of memory length on strategy success in a game-theoretic model.

Contribution

It systematically analyzes the effects of different update schemes and memory lengths on competitive learning, identifying phase behavior and universality classes.

Findings

Phase diagram shows disordered and ordered phases with coexistence.

Critical exponents match the generalized voter model universality class.

Long memory can offset the disadvantage of a inferior strategy.

Abstract

We examine the effects of memory and different updating paradigms in a game-theoretic model of competitive learning, where agents are influenced in their choice of strategy by both the choices made by, and the consequent success rates of, their immediate neighbours. We apply parallel and sequential updates in all possible combinations to the two competing rules, and find, typically, that the phase diagram of the model consists of a disordered phase separating two ordered phases at coexistence. A major result is that the corresponding critical exponents belong to the generalised universality class of the voter model. When the two strategies are distinct but not too different, we find the expected linear response behaviour as a function of their difference.Finally, we look at the extreme situation when a superior strategy, accompanied by a short memory of earlier outcomes, is pitted against its inverse; interestingly, we find that a long memory of earlier outcomes can occasionally compensate for the choice of a globally inferior strategy.