大围长图的囚徒困境
Prisoner's Dilemma on Graphs with Large Girth
摘要：
我们研究了在网络中个人扮演囚徒困境的群体中合作的演化。网络中的每个节点都对应着一个人在重复博弈中选择合作还是背叛。参与者通过模仿那些有更高收益的邻居来修改他们的行为。我们表明，当相互作用发生在图与大周长，合作更有可能出现。另一方面，在有许多长度为3和4的圈的图中，背叛传播得更快。我们的分析的一个关键思想是，我们的动态可以被看作是一个扰动的选民模型。我们写相应的马尔可夫链的转移核的投票模型中的成对相关性。我们分析了成对的相关性，并表明，在图中相对较大的围长，合作者集群和相互帮助。
英文摘要：
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.
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