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We study the evolution of cooperation in populations where individuals play prisoners dilemma on a network. Every node of the network corresponds on an individual choosing whether to cooperate or defect in a repeated game. The players revise their actions by imitating those neighbors who have higher payoffs. We show that when the interactions take place on graphs with large girth, cooperation is more likely to emerge. On the flip side, in graphs with many cycles of length 3 and 4, defection spreads more rapidly. One of the key ideas of our analysis is that our dynamics can be seen as a perturbation of the voter model. We write the transition kernel of the corresponding Markov chain in terms of the pairwise correlations in the voter model. We analyze the pairwise correlation and show that in graphs with relatively large girth, cooperators cluster and help each other.
Two-player games have had a long and fruitful history of applications stretching across the social, biological, and physical sciences. Most applications of two-player games assume synchronous decisions or moves even when the games are iterated. But d
Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic attributes
We show that every n-vertex cubic graph with girth at least g have domination number at most 0.299871n+O(n/g)<3n/10+O(n/g).
An induced forest of a graph G is an acyclic induced subgraph of G. The present paper is devoted to the analysis of a simple randomised algorithm that grows an induced forest in a regular graph. The expected size of the forest it outputs provides a l
Influence maximization, defined as a problem of finding a set of seed nodes to trigger a maximized spread of influence, is crucial to viral marketing on social networks. For practical viral marketing on large scale social networks, it is required tha