Two-strategy games with time constraints on regular graphs

JOURNAL OF THEORETICAL BIOLOGY

卷:506

Article

Broom, Mark¹  Krivan, Vlastimil^2,3 

[1] City Univ London, Dept Math, London, England

[2] Univ South Bohemia, Fac Sci, Ctr Math Biol, Dept Math, Branisovska 1760, Ceske Budejovice 37005, Czech Republic

[3] Czech Acad Sci, Biol Ctr, Inst Entomol, Branisovska 31, Ceske Budejovice 37005, Czech Republic

关键词: Birth-death and death-birth updating;    Evolutionary game theory;    Games on regular graphs;    Hawk-Dove game;    Prisoner's dilemma;   

DOI  :  10.1016/j.jtbi.2020.110426

来源: Elsevier

【 摘 要 】

Evolutionary game theory is a powerful method for modelling animal conflicts. The original evolutionary game models were used to explain specific biological features of interest, such as the existence of ritualised contests, and were necessarily simple models that ignored many properties of real populations, including the duration of events and spatial and related structural effects. Both of these areas have subsequently received much attention. Spatial and structural effects have been considered in evolutionary graph theory, and a significant body of literature has been built up to deal with situations where the population is not homogeneous. More recently a theory of time constraints has been developed to take account of the fact that different events can take different times, and that interaction times can explicitly depend upon selected strategies, which can, in turn, influence the distribution of different opponent types within the population. Here, for the first time, we build a model of time constraint games which explicitly considers a spatial population, by considering a population evolving on an underlying graph, using two graph dynamics, birth-death and death-birth. We consider one short time scale along which frequencies of pairs and singles change as individuals interact with their neighbours, and another, evolutionary time scale, along which frequencies of strategies change in the population. We show that for graphs with large degree, both dynamics reproduce recent results from well-mixed time constraint models, including two ESSs being common in Hawk-Dove and Prisoner's Dilemma games, but for low degree there can be marked differences. For birth-death processes the effect of the graph degree is small, whereas for death-birth dynamics there is a large effect. The general prediction for both Hawk-Dove and Prisoner's dilemma games is that as the graph degree decreases, i.e., as the number of neighbours decreases, mixed ESS do appear. In particular, for the Prisoner's dilemma game this means that cooperation is easier to establish in situations where individuals have low number of neighbours. We thus see that solutions depend non-trivially on the combination of graph degree, dynamics and game. (C) 2020 Elsevier Ltd. All rights reserved.

【 授权许可】

Free