Replicator Equation and the Evolution of Cooperation on Regular Communities

Replicator equation on networks with degree regular communities

“…In this paper I presented an extension of my previous work ( Cassese 2017 ), providing a version of the replicator equation for a family of graphs characterised by degree-regular communities. As examples of possible application of this equation, here I study the evolutionary dynamics of three game classes: Prisoner’s dilemma, Hawk-Dove and Coordination games.…”

“…Comparing the difference between the bounds and the true thresholds numerically, it appears that this difference is always greater for imitation than birth-death, meaning that imitation promotes cooperation more than birth-death for the Prisoner’s dilemma. In ( Cassese 2017 ) I also show that there can be cases where cooperation and defection coexist, so there is a stable mixed equilibrium. Using a colour map like in Fig.…”

“…Notice that the above conditions say that the benefit-cost ratio sufficient to sustain cooperation in equilibrium increases with average connectivity in a graphs with regular communities. These conditions are sufficient but not necessary, as I proved in more details in ( Cassese 2017 ), given that the true benefit-cost thresholds that promote cooperations under the two different mechanisms are bounded above by and respectively, so a graph with regular communities and degree distribution is more favourable to cooperation than a graph with the same degree distribution where the communities are disconnected, so that the graph has as many connected components as the number of communities. Comparing the difference between the bounds and the true thresholds numerically, it appears that this difference is always greater for imitation than birth-death, meaning that imitation promotes cooperation more than birth-death for the Prisoner’s dilemma.…”

“…where k i is the degree of nodes inside community i and is the probability that a node is in a community with degree k i , or the fraction of nodes in a community with degree k i , so that the global dynamic is a weighted average of the local dynamics on each community ( Cassese 2017 ).…”

PUEGM: A Method of User Revenue Selection Based on a Publisher-User Evolutionary Game Model for Mobile Crowdsensing

“…We use qifalse(tfalse) to indicate the proportion of user who choose the strategy uwi, where true∑i=1nqifalse(tfalse)=1. For a certain data quality optional strategy uwi, the dynamic rate of change can be denoted by replicator dynamic equation [25], which is written as:ufalse(qfalse)=dqifalse(tfalse)dt=q*false(Buwi−trueBu¯false).…”