期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：1
页码：399-427
DOI：10.30757/ALEA.v16-15
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：This paper studies a variant of the multi-type contact process as amodel for the competition between cooperators and defectors. Regardless of theirtype, individuals die at rate one. Defectors give birth at a fixed rate whereas cooperatorsgive birth at a rate that increases linearly with the number of nearby cooperators.In particular, it is assumed that only cooperators benefit from cooperators,which is referred to as kin-recognition in the ecological literature. To understandhow the inclusion of space in the form of local interactions affects the dynamics,the results for the interacting particle system are compared with their counterpartfor the non-spatial mean-field model. Due to some monotonicity with respect tothe parameters, both the spatial and non-spatial models exhibit a unique phasetransition. Our analysis shows however a major difference: In the spatial model,when cooperation is strong enough, the cooperators out-compete the defectors evenwhen starting at arbitrarily low density. In contrast, regardless of the strength ofcooperation, when the initial density of cooperators is too low, the defectors outcompetethe cooperators in the non-spatial model. In particular, when cooperationis sufficiently strong, the cooperators can invade the defectors in their equilibrium inthe spatial model but not in the non-spatial model, showing that space in the formof local interactions promotes cooperation. This result is consistent with previousresults in the literature of interacting particle systems, but our work also showsan interesting novel aspect: in contrast with the inclusion of local interactions, theinclusion of spontaneous deaths promotes defection.
关键词：Multi;type contact process; oriented site percolation; block construc;;tion; evolutionary game theory; prisoner’s dilemma; cooperator; defector;
