Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma
Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma
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DOI：
10.1016/j.jtbi.2004.06.003
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发表时间：
2004-11-07
影响因子：
2
通讯作者：
Doebeli, M
中科院分区：
文献类型：
--
作者：
Ifti, M;Killingback, T;Doebeli, M
囚徒困境是一种两人博弈，参与者要么合作，要么背叛，是研究合作演化的常见范式。在真实的情况下，合作几乎从来不是全有或全无。这一观察是连续囚徒困境的动机，在这个困境中，个体表现出不同程度的合作。众所周知，在空间结构的存在下，当个体与他们的邻居“对抗”（即互动），并“比较”（“学习”）他们。合作投资可以发展到相当高的水平。在这里，我们研究的影响，增加neiahbourhood的大小：我们发现，平均场的限制没有合作达到一个临界邻域大小约5个邻居在每一边的摩尔附近，这并不依赖于空间晶格的大小。我们还发现了相关的结果，在一个网络的球员，临界平均度（邻居的数量）的节点，背叛是最终状态不依赖于网络的大小，但只依赖于网络的拓扑结构。这个临界平均度是相当高的（约10倍）集群（社会）网络，比分布式随机网络。这一结果加强了集群是使合作的发展和维持成为可能的机制的论点。在晶格拓扑结构中，据观察，当“互动”和“学习”的邻域大小相差超过0.5，合作是不可持续的，即使是低于平均场极限的缺陷的邻域大小。我们还研究了邻里规模的演变，以及投资水平。在这里，我们观察到，一系列的互动和学习的邻域收敛，并达到了相当程度的平均投资的最终合作状态。(C)2004爱思唯尔有限公司保留所有权利。
The Prisoner's Dilemma, a two-person game in which the players can either cooperate or defect, is a common paradigm for studying the evolution of cooperation. In real situations cooperation is almost never all or nothing. This observation is the motivation for the Continuous Prisoner's Dilemma, in which individuals exhibit variable degrees of cooperation. It is known that in the presence of spatial structure, when individuals "play against" (i.e. interact with) their neighbours, and "compare to" ("learn from") them. cooperative investments can evolve to considerable levels. Here, we examine the effect of increasing the neiahbourhood size: we find that the mean-field limit of no cooperation is reached for a critical neighbourhood size of about five neighbours on each side in a Moore neighbourhood, which does not depend on the size of the spatial lattice. We also find the related result that in a network of players, the critical average degree (number of neighbours) of nodes for which defection is the final state does not depend on network size, but only on the network topology. This critical average degree is considerably (about 10 times) higher for clustered (social) networks, than for distributed random networks. This result strengthens the argument that clustering is the mechanism which makes the development and maintenance of the cooperation possible. In the lattice topology, it is observed that when the neighbourhood sizes for "interacting" and "learning" differ by more than 0.5, cooperation is not sustainable, even for neighbourhood sizes that are below the mean-field limit of defection. We also study the evolution of neighbourhood sizes, as well as investment level. Here, we observe that the series of the interaction and learning neighbourhoods converge, and a final cooperative state with considerable levels of average investment is achieved. (C) 2004 Elsevier Ltd. All rights reserved.