From pairwise to group interactions in games of cyclic dominance

Szolnoki, Attila and Vukov, Jeromos and Perc, Matjaž (2014) From pairwise to group interactions in games of cyclic dominance. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR AND SOFT MATTER PHYSICS, 89 (6). 062125. ISSN 1539-3755

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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 aswith 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.

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