Abstract
We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when different strategies coexist, can be understood through the geometric behavior of clusters involving four effective strategies competing cyclically,without neutral states. Moreover, the existence of strong finite-size effects, a form of the survival of the weakest effect, is related to a percolation crossover. These results may be generic and of relevance to other bimatrix games.
Highlights
Cyclic dominance is an important mechanism underlying the coexistence of competing species or strategies in several different contexts [1,2]
When one or more intransitive loops are present in the effective flux graph that contains information on how those species interact, the hierarchy introduced by other transitive loops may be attenuated, enhancing the conditions for the persistent survival of several species
One example is three-strategies games with optional participation: not explicit in the payoff matrix, dominance emerges in the presence of these agents that do not follow the rules of the game and prefer, instead, to earn a smaller payoff [3]. Another scenario in which cyclic dominance appears is among preys and predators choosing, respectively, their hunt and defense strategy while trying to outcompete each other [4]
Summary
Cyclic dominance is an important mechanism underlying the coexistence of competing species or strategies in several different contexts [1,2]. One example is three-strategies games with optional participation: not explicit in the payoff matrix, dominance emerges in the presence of these agents that do not follow the rules of the game and prefer, instead, to earn a smaller payoff [3] Another scenario in which cyclic dominance appears is among preys and predators choosing, respectively, their hunt and defense strategy while trying to outcompete each other [4]. Cazaubiel et al [4] revisited the model and proposed a spatial version with local interactions and binary strategies, unveiling the mechanism underlying the stability of the coexistence phase In this version, all predators in site i may form a single group (xi = 1). These strategies obey cyclic dominance relations leading to persistent coexistence for a broad set of parameters [4] This behavior is reminiscent of the generalizations of the RPS game with more than three species [1,2]. The existence of a size dependent percolation crossover helps to understand, as a realization of the survival of the weakest principle [36], the strong finite-size effects presented by the model
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