捷径连接和噪声对带志愿者的囚徒困境博弈演化的影响

Effects of Noises and Shortcut Connections on the Evolutionary Prisoner's Dilemma Games with Voluntary Participation

关于双层网络上的博弈研究很少,尤其带志愿者参加的囚徒博弈研究不曾出现过.利用蒙特卡罗数值模拟方法研究带有志愿者参加的囚徒困境博弈模型在双层网络上的演化,研究结果表明:①当捷径连接不存在时,对于较小的背叛诱惑值随着噪声水平的增加合作密度出现多个峰值相干共振现象,较大背叛诱惑值出现单峰相干共振现象;②当存在捷径连接时,原来的多峰相干共振现象被单峰共振现象取代,对较大的背叛诱惑值当增边概率p足够大时会出现2个极大值;③中等程度噪声水平和较小的背叛诱惑值下随增边概率p增加达到一个阈值后志愿者消失,这时增边概率p有利于合作程度的提高;增边概率p小于这个阈值时3种策略共存,由于3种策略的相互入侵随p的变化会得到更复杂的结果.

Adopting two dimensional Newman-Watts small-world networks,we study the evolution of co- operation in the voluntary prisoner＇s dilemma game with two-layered graphs. Based on the Monte Carlo simulations,we investigate the effects of noises and the topology p of learning graphs. Some interesting re- suits are found： （1） Multi-peaks of density of cooperation vs. k are observed;（2） The topology p of learning graphs favors cooperation instead of defection when loners are extinct;Q There is much more nontrivial dependence of density of cooperation vs. p when three strategies coexist.