摘要
解释合作行为的演化一直是生命科学及社会学研究的重要问题之一。经典理论研究大都关注于合作双方对等的情况。然而,在合作系统中的合作双方通常是不对等的,由此可带来博弈双方支付的非对称并影响合作双方的合作行为。该文基于经典的"鹰鸽博弈"模型,同时考虑非对称性相互关系和资源压力的影响,建立了具有强弱之分的四策略(实力强且合作、实力强且不合作、实力弱且合作和实力弱且不合作)非对称博弈模型。结合演化博弈理论及动力系统稳定性理论分析发现:在系统达到稳定状态时,四种策略的比例变化显著地依赖于博弈双方的强弱之比、资源压力及冲突的单位成本收益。对模型的进一步分析显示,当资源充足时,实力强且合作的比例与冲突的单位成本收益负相关;而实力强且不合作、实力弱且不合作的比例都与冲突的单位成本收益正相关,并且随着系统强弱对比增加,实力强且合作及实力强且不合作的比例均增加,而实力弱且不合作的比例将减小。当资源短缺时,模型得出一个有趣的结论,即随着博弈双方的强弱之比的变化,经典的"智猪博弈"与"鹰鸽博弈"可相互转化,该结论将能为不同均衡状态之间的相互转化给出一个动力学解释。
Explaining the evolution of cooperation remains one of the important problems in both biology and social science. Classical theories mainly based on an assumption that cooperative players are symmetrically interacted. However, almost all the well-studied systems showed that cooperative players are in fact asymmetrically interacted and that asymmetric interaction might greatly affect cooperation behavior of the involved players. Considering the asymmetric interaction and the selection pressure of resources, we present a model that possesses four strategies： strength- cooperation （SC）, strength-defection （SD）, weakness-cooperation （WC） and weakness-defection （WD）. Combining evolutionary game theory with dynamical stability theory, we fend that the evolutionary results closely depend on the asymmetric interaction and selection pressure of resources as well as cost-to-benefit ratio of conflict. When the common resources are plentiful, the cost-to-benefit ratio of conflict is negatively correlated with the probability of SC, while it is positively correlated with the probability of SD and WD. With increasing the strength ratio between the strong and weak players, the proportion of SC and SD will increase, while the proportion of WD will reduce. The model developed here has intrinsically integrated Boxed Pigs game and Hawk-Dove game. When the common resource is at shortage, the Boxed Pigs game will transform into Hawk-Dove game under the increase of the strength ratio between the strong and weak players.
基金
国家自然科学基金资助项目具有P-F性质矩阵及其相关矩阵的性质
算法和应用研究(10961027)
合作系统中非对称性和互惠(或亲缘)关系的相互作用研究(71161020)
种间合作系统稳定性维持机制的探讨(31170408)
云南省自然科学基金(2009CD104)
中国科学院优秀青年科技专项(KSCX2-EW-Q-9)
关键词
非对称
鹰鸽博弈
复制动态方程
进化稳定策略
智猪博弈
Asymmetric
Hawk-Dove game
Replicator equation
Evolutionarily stable strategy
Boxed pigs game
