Evolving multiplayer networks: Modelling the evolution of cooperation in a mobile population

Abstract

We consider a finite population of individuals that can move through a structured environment using our previously developed flexible evolutionary framework. In the current paper the behaviour of the individuals follows a Markov movement model where decisions about whether they should stay or leave depends upon the group of individuals they are with at present. The interaction between individuals is modelled using a public goods game. We demonstrate that cooperation can evolve when there is a cost associated with movement. Combining the movement cost with a larger population size has a positive effect on the evolution of cooperation. Moreover, increasing the exploration time, which is the amount of time an individual is allowed to explore its environment, also has a positive effect. Unusually, we find that the evolutionary dynamics used does not have a significant effect on these results.2010 Mathematics Subject Classification. 91A22, 60J10, 92D15.

The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

“…Selection no longer favours defectors even in small populations, and selection favours cooperators for higher values of the movement cost (up to λ = 0.5). These outcomes are consistent with the results in [36] Increasing the reward-to-cost ratio allows selection to favour cooperators for all movement costs. Conversely, decreasing the reward-to-cost ratio allows selection to favour defectors even in large populations.…”

“…In this paper, we build upon the work of [36], the first history-dependent model of the evolutionary framework of [32], which allows for general multi-player interactions and structured populations. Here (and in [36]) a mobile population moves around a territory in the form of a network, with groups of individuals interacting at the nodes. Movement is Markov, with the place an individual moves to next depending upon both current position and the composition of their current group.…”

“…Here, we provide a brief overview of the framework of Broom & Rychtář [32]. We consider only sufficient detail to understand the current paper, and we use terminology as in [36], which was slightly different from [32] because it is more natural for the Markov models considered here. The model is broken down into four key components: population structure, movement, fitness and evolutionary dynamics.…”

Dynamics of multiplayer games on complex networks using territorial interactions

“…Linearity with the temperature can partly be explained by the fact that for the models in this paper an individual's temperature effectively reduces to the probability of it not being alone at the replacement event and in the contests that lead to payoffs (note that these two need not be the same [38] and that a more complex temperature concept was needed when subpopulations formed on nodes [37]). Thus for small temperatures, mean temperature is strongly correlated with the intensity of selection, and the fixation probabilities are close to straight lines at a temperature of 0.…”

“…Thus there is a need for models of evolution on structured populations that incorporate multiplayer games of varying numbers of players. Broom and Rychtar developed a general framework for analyzing such multi-player games in structured populations in [26], with further work on this in [35][36][37][38]. In particular, [36] considered evolution using three classical game scenarios (Hawk-Dove, Prisoner's Dilemma and fixed fitness) in structured populations using the Invasion Process dynamics for some simple cases, using the "territorial raider" model, which used an underlying graphical structure as its basis [39].…”