Ecological public goods games: Cooperation and bifurcation
Ecological public goods games: Cooperation and bifurcation
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DOI：
10.1016/j.tpb.2007.11.007
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发表时间：
2008-03-01
影响因子：
1.4
通讯作者：
Doebeli, Michael
中科院分区：
文献类型：
--
作者：
Hauert, Christoph;Wakano, Joe Yuichiro;Doebeli, Michael
公共物品博弈是研究合作起源和维持的最流行的模型之一。在其最简单的形式中，这个进化博弈有两个区域：如果乘积因子r小于相互作用小组的大小N，则叛逃进入固定；而如果乘积因子r大于相互作用小组的大小N，则合作进入固定。[Hauert，C.，Holmes，M.，Doebeli，M.，2006 a.进化博弈与种群动态：维持公共物品博弈中的合作。程序R.Soc.朗德。通过将进化博弈的收益视为人口动态模型中的出生率，引入了生态公共产品博弈。这导致了生态和进化动力学之间的反馈：如果叛逃者普遍存在，出生率低，人口密度下降，这导致公共产品博弈中较小的互动群体，从而导致合作者的主导地位，伴随而来的是出生率和人口密度的增加。这种反馈可以导致合作者和叛逃者之间稳定的共存。本文对生态公共产品博弈的动力学进行了详细的分析，结果表明该模型存在各种类型的分支，包括超临界Hopf分支，这些分支导致稳定的极限环，从而导致合作者和叛逆者的振荡共存。这些结果表明，将种群动态纳入进化博弈可以对合作的进化动力学产生重要影响。(C)2007 Elsevier Inc.保留所有权利。
The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the-Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation. (C) 2007 Elsevier Inc. All rights reserved.