Strategy dependent learning activity in cyclic dominant systems

TL;DR

This paper investigates how reducing learning activity in a specific strategy within cyclic dominant systems affects the overall dynamics, revealing counterintuitive increases in the prevalence of predator strategies.

Contribution

It introduces a model where a strategy's reluctance to change influences the system's equilibrium, highlighting non-linear effects in cyclic dominance scenarios.

Findings

Reduced learning activity in one strategy increases the prevalence of its predator.

The effect is non-linear and depends on model specifics.

Lowering invasion rates can promote the growth of certain strategies.

Abstract

The prototype of a cyclic dominant system is the so-called rock-scissors-paper game, but similar relation among competing strategies can be identified in several other models of evolutionary game theory. In this work we assume that a specific strategy from the available set is reluctant to adopt alternative states, hence the related learning activity is reduced no matter which other strategy is considered for adoption. Paradoxically, this modification of the basic model will primarily elevate the stationary fraction of another strategy who is the virtual predator of the one with reduced learning activity. This general reaction of the studied systems is in agreement with our understanding about Lotka-Volterra type cyclic dominant systems where lowering the invasion rate between a source and target species promotes the growth of former population. The observed effect is highly non-linear because the effective invasion rates between strategies may depend sensitively on the details of the actual model.