囚徒困境中基于非均匀连接的促合作控制设计

The controller design for promoting the evolution of cooperation in the prisoner's dilemma based on the non-uniform interaction rates

本文研究"囚徒困境"中促进合作演化的机制,设计"合作识别"和"背叛识别"两种控制形式,并分析合作在相应控制之下的演化路径问题.在合作识别控制设计中,通过将博弈群体分为合作者子群体和合作者与背叛者共存子群体,形成连接率依赖于个体策略的"非均匀连接",以保护合作的方式抑制背叛,促进合作演化;在背叛识别控制设计中,以惩罚背叛的方式鼓励合作.文章指出,合作识别控制设计能在合作率较低时促进合作,但不能使合作成为演化稳定策略(ESS);背叛识别控制设计能在合作率较高时使合作成为ESS,但是背叛总是该控制下的ESS.结合"合作识别"控制与"背叛识别"控制,本文设计一种切换控制,使得合作是"囚徒困境"博弈的唯一ESS.仿真给出不同要求下的控制律设计,分析不同切换选择对合作演化路径的影响.

This paper focuses on the mechanisms that promote the evolution of cooperation in the pris- oner＇s dilemma. The controls based on cooperation recognition and defection recognition are designed and the evolution paths of cooperation under different controls are analyzed. Under the control based on cooperation recognition, the population is divided into two parts： cooperation-subpopulation and cooperation- and-defection-subpopulation. Non-uniform interaction rates is defined as the probability of interaction between two players is dependent of their strategy. It can increase the interaction rates between two subpopulations with the same strategy. It promotes the evolution of cooperation by protecting cooperation. Under the other control, based on defection recognition, the evolution of cooperation is promoted by punishing defection. We find that the control based on cooperation recognition can promote cooperation when the cooperation rate is low. But cooperation can＇t become the evolutionarily stable strategy （ESS） under this control. The control based on the defection recognition can translate cooperation to ESS with highly initial cooperation rate, but defection will always be ESS. So we design a new control, called switching control. Based on these two controls, cooperation is translated to the only one ESS. The experiments show the affection of different switching control on the evolution path of cooperation.