Today I read a paper titled “Prisoner’s Dilemma on Graphs with Large Girth”
The abstract is:
We study the evolution of cooperation in populations where individuals play prisoner’s 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