Evolutionary dynamics under periodic switching of update rules on regular networks

TL;DR

This paper investigates how periodic switching of strategy update rules on regular networks influences the emergence of cooperation in evolutionary games, providing a theoretical framework and validating results through numerical examples.

Contribution

It introduces a novel theoretical framework using switched system theory to analyze the effects of periodically switching update rules on cooperation.

Findings

Periodic switching can promote cooperation under certain conditions.

Theoretical conditions for cooperation emergence are derived and validated.

Numerical examples confirm the effectiveness of switching strategies.

Abstract

Microscopic strategy update rules play an important role in the evolutionary dynamics of cooperation among interacting agents on complex networks. Many previous related works only consider one \emph{fixed} rule, while in the real world, individuals may switch, sometimes periodically, between rules. It is of particular theoretical interest to investigate under what conditions the periodic switching of strategy update rules facilitates the emergence of cooperation. To answer this question, we study the evolutionary prisoner's dilemma game on regular networks where agents can periodically switch their strategy update rules. We accordingly develop a theoretical framework of this periodically switched system, where the replicator equation corresponding to each specific microscopic update rule is used for describing the subsystem, and all the subsystems are activated in sequence. By utilizing switched system theory, we identify the theoretical condition for the emergence of cooperative behavior. Under this condition, we have proved that the periodically switched system with different switching rules can converge to the full cooperation state. Finally, we consider an example where two strategy update rules, that is, the imitation and pairwise-comparison updating, are periodically switched, and find that our numerical calculations validate our theoretical results.