title: On the preservation of cooperation in two-strategy games with nonlocal interactions.
abstract: Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models.
authors.affiliation: Department of Economics, Social Sciences University of Ankara, Ankara, Turkey. Electronic address: ozgur.aydogmus@asbu.edu.tr.
authors.forename: Ozgur
authors.initials: O
authors.lastname: Aydogmus
authors.affiliation: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA. Electronic address: riczw@stat.colostate.edu.
authors.forename: Wen
authors.initials: W
authors.lastname: Zhou
authors.affiliation: Sciences and Mathematics Faculty, College of Letters and Sciences, Arizona State University, Mesa, AZ 85212, USA. Electronic address: yun.kang@asu.edu.
authors.forename: Yun
authors.initials: Y
authors.lastname: Kang
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003299:Cooperative Behavior; D017753:Ecosystem; D005716:Game Theory; D006801:Humans; D011157:Population Dynamics
keywords: Evolutionary game; Integro-differential replicator equations; Nonlocal interaction; Selections in genetic games