Szolnoki Attila, Vukov Jeromos, Perc Matjaž
Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, Hungary.
Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062125. doi: 10.1103/PhysRevE.89.062125. Epub 2014 Jun 18.
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.
我们研究结构化种群中的剪刀石头布游戏，其中入侵率决定个体收益，而个体收益支配着策略变化的过程。如果每个潜在入侵的收益源于单个两两相互作用，那么该游戏的传统版本就会重现。然而，将入侵率转化为收益也允许使用更大的相互作用范围。因此，除了传统的两两相互作用外，我们还考虑与所有最近邻以及所有最近邻和次近邻的同时相互作用，从而在循环优势博弈中有效地从单对相互作用转变为群体相互作用。我们表明，相互作用范围的差异不仅会影响策略的稳定比例，还会影响它们的优势关系。因此，从两两相互作用到群体相互作用的转变可以减缓甚至逆转竞争策略之间的入侵方向。与进化社会困境一样，在循环优势博弈中，由于群体相互作用而产生的间接多点相互作用也起着关键作用。我们的结果表明，除了入侵率之外，相互作用范围对于维持循环竞争策略之间的生物多样性至少同样重要。
