Self-organizing patterns in an evolutionary rock-paper-scissors game for stochastic synchronized strategy updates

Abstract

We study a spatial evolutionary rock-paper-scissors game with synchronized strategy updating. Players gain their payoff from games with their four neighbors on a square lattice and can update their strategies simultaneously according to the logit rule, which is the noisy version of the best-response dynamics. For the synchronized strategy update two types of global oscillations (with an ordered strategy arrangement and periods of three and six generations) can occur in this system in the zero noise limit. At low noise values, all nine oscillating phases are present in the system by forming a self-organizing spatial pattern due to the comprising invasion and speciation processes along the interfaces separating the different domains.

Evolutionary potential games on lattices

“…The analysis of the competition between strategy associations is generally based on models with random sequential imitation type evolutionary rule that may even be applied simultaneously for several systems [348] when the models become similar to stochastic cellular automata [349,350]. The spatial rock-paper-scissor game with a synchronized stochastic logit update [351] has demonstrated the appearance of chimera states which have been intensively studied in the literature of coupled spatial oscillators [352,353,354,355,356]. For the repeated two-player rock-paper-scissors game the synchronized logit rule at low noises results in cyclic choices [e.g.…”

A theoretical approach to understand spatial organization in complex ecologies

“…Realistic ecologies, however, are endowed with complex interaction networks that can not be captured fully by only considering symmetric networks. As such it is important to develop theoretical approaches that allow to understand the dynamics of general networks (Szabó et al, 2007b;Lütz et al, 2013;Provata et al, 1999;Vandermeer and Yitbarek, 2012;Knebel et al, 2013;Dobrinevski et al, 2014;Rulquin and Arenzon, 2014;Varga et al, 2014;Szabó et al, 2015;Daly et al, 2015;Szolnoki and Perc, 2015) and their effects on biodiversity, correlations, and spatio-temporal patterns.…”

Pattern formations driven by cyclic interactions: A brief review of recent developments

“…Needless to say, such a brief review cannot be complete and is unable to give account for all possible directions, like the consequences of mutant species [61,62], environmental randomness [63,64], the role of myopic strategy update [65], or the case of metapopulation models [66][67][68][69]. Hence, we refer the interested reader to the original works for further details.…”