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Games 2017, 8(1), 10; doi:10.3390/g8010010

Cyclic Competition and Percolation in Grouping Predator-Prey Populations

1
Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil
2
Normale Supérieure, International Center of Fundamental Physics, 45 Rue d’Ulm, 75005 Paris, France
*
Author to whom correspondence should be addressed.
Received: 8 December 2016 / Accepted: 17 January 2017 / Published: 2 February 2017
(This article belongs to the Special Issue Evolutionary Games and Statistical Physics of Social Networks)
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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. View Full-Text
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Lütz, A.F.; Cazaubiel, A.; Arenzon, J.J. Cyclic Competition and Percolation in Grouping Predator-Prey Populations. Games 2017, 8, 10.

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