{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:43:47Z","timestamp":1760784227407,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,2]],"date-time":"2017-02-02T00:00:00Z","timestamp":1485993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004263","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado do Rio Grande do Sul","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004263","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Instituto Nacional de Ci\u00eancia e Tecnologia Sistemas Complexos"},{"name":"Ecole Normale Superieure Paris"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>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. Speci\ufb01cally, 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 \ufb01nite-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.<\/jats:p>","DOI":"10.3390\/g8010010","type":"journal-article","created":{"date-parts":[[2017,2,2]],"date-time":"2017-02-02T11:24:06Z","timestamp":1486034646000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Cyclic Competition and Percolation in Grouping Predator-Prey Populations"],"prefix":"10.3390","volume":"8","author":[{"given":"Alessandra","family":"L\u00fctz","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil"}]},{"given":"Annette","family":"Cazaubiel","sequence":"additional","affiliation":[{"name":"Normale Sup\u00e9rieure, International Center of Fundamental Physics, 45 Rue d\u2019Ulm, 75005 Paris, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8373-6475","authenticated-orcid":false,"given":"Jeferson","family":"Arenzon","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.physrep.2007.04.004","article-title":"Evolutionary games on graphs","volume":"446","year":"2007","journal-title":"Phys. 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