From pairwise to group interactions in games of cyclic dominance

TL;DR

This paper investigates how expanding the interaction range from pairwise to group interactions in cyclic dominance games affects strategy dynamics, revealing that interaction range significantly influences strategy prevalence and dominance relations.

Contribution

It introduces the analysis of group interactions in cyclic dominance games, showing their impact on strategy dynamics beyond traditional pairwise models.

Findings

Group interactions alter stationary strategy fractions.

Interaction range can reverse invasion directions.

Group interactions are crucial for biodiversity maintenance.

Abstract

We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change. The traditional version of the game is recovered if the payoffs for each potential invasion stem from a single pairwise interaction. However, the transformation of invasion rates to payoffs also allows the usage of larger interaction ranges. In addition to the traditional pairwise interaction, we therefore consider simultaneous interactions with all nearest neighbors, as well as with all nearest and next-nearest neighbors, thus effectively going from single pair to group interactions in games of cyclic dominance. We show that differences in the interaction range affect not only the stationary fractions of strategies, but also their relations of dominance. The transition from pairwise to group interactions can thus decelerate and even revert the direction of the invasion between the competing strategies. Like in evolutionary social dilemmas, in games of cyclic dominance too the indirect multipoint interactions that are due to group interactions hence play a pivotal role. Our results indicate that, in addition to the invasion rates, the interaction range is at least as important for the maintenance of biodiversity among cyclically competing strategies.