时间尺度与选择倾向性协同作用下的演化博弈模型
|
摘要
针对合作行为的涌现与维持问题,基于演化博弈理论和网络理论,提出了一种促进合作的演化博弈模型。该模型同时将时间尺度、选择倾向性引入到演化博弈中。在初始化阶段,根据持有策略的时间尺度将个体分为两种类型:一种个体在每个时间步都进行策略更新;另一种个体在每一轮博弈后,以某种概率来决定是否进行策略更新。在策略更新阶段,模型用个体对周围邻居的贡献来表征他的声誉,并假设参与博弈的个体倾向于学习具有较好声誉邻居的策略。仿真实验结果表明,所提出的时间尺度与选择倾向性协同作用下的演化博弈模型中,合作行为能够在群体中维持;惰性个体的存在不利于合作的涌现,但是个体的非理性行为反而能够促进合作。
Considering emergence and maintenance of cooperative behavior, based on evolutionary game theory and network theory, an evolutionary game model which can promote cooperation was proposed. In the proposed model, time scale and selection preference were introduced simultaneously into evolutionary game. In initialization phase, players were segmented into two categories according to their time scales of the strategies. Players in one category updated their strategies in each round, while players in the other category determined wether to update their strategies according to certain probability after every round of game. In strategy updating phase, the reputation of a player was determined by his distribution to his neighbors, and all players perfered to learn the strategies of neighbors with good reputation. The simulation experimental results show that, in the proposed evolutionary game model under synergistic effect of time scale and selection preference, cooperative behavior can be maintained in the group, the players with inertia hinders the emergence of cooperation, but the irrational behavior of players can promote cooperation.
Considering emergence and maintenance of cooperative behavior, based on evolutionary game theory and network theory, an evolutionary game model which can promote cooperation was proposed. In the proposed model, time scale and selection preference were introduced simultaneously into evolutionary game. In initialization phase, players were segmented into two categories according to their time scales of the strategies. Players in one category updated their strategies in each round, while players in the other category determined wether to update their strategies according to certain probability after every round of game. In strategy updating phase, the reputation of a player was determined by his distribution to his neighbors, and all players perfered to learn the strategies of neighbors with good reputation. The simulation experimental results show that, in the proposed evolutionary game model under synergistic effect of time scale and selection preference, cooperative behavior can be maintained in the group, the players with inertia hinders the emergence of cooperation, but the irrational behavior of players can promote cooperation.
引文
[1]荣智海,吴枝喜,王文旭.共演博弈下网络合作动力学研究进展[J].电子科技大学学报,2013,42(1):10-22.(RONG Z H,WU Z X,WANG W X.Research on the networked cooperative dynamics of coevolutionary games[J].Journal of University of Electronic Science and Technology of China,2013,42(1):10-22.)
[2]NOWAK M A,MAY R M.Evolutionary games and spatial chaos[J].Nature,1992,359(6398):826-829.
[3]NOWAK M A,MAY R M.The spatial dilemmas of evolution[J].International Journal of Bifurcation and Chaos,1993,3(1):35-78.
[4]WU Z X,RONG Z H,HOLME P.Diversity of reproduction time scale promotes cooperation in spatial prisoner's dilemma games[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,2009,80(3 Pt 2):036106.
[5]RONG Z H,WU Z X,CHEN G R.Coevolution of strategy-selection time scale and cooperation in spatial prisoner's dilemma game[J].Europhysics Letters,2013,102(6):68005.
[6]JIA D Y,JIN J H,DU C P,et al.Effects of inertia on the evolution of cooperation in the voluntary prisoner's dilemma game[J].Physica A:Statistical Mechanics and its Applications,2018,509:817-826.
[7]WU Z X,XU X J,HUANG Z G,et al.Evolutionary prisoner's dilemma game with dynamic preferential selection[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,2006,74(2):021107.
[8]WANG Z,PERC M.Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,2010,82(2 Pt 1):021115.
[9]XIA C Y,DING S,WANG C J,et al.Risk analysis and enhancement of cooperation yielded by the individual reputation in the spatial public goods game[J].IEEE Systems Journal,2017,11(3):1516-1525.
[10]CHEN M H,WANG L,SUN S W,et al.Evolution of cooperation in the spatial public goods game with adaptive reputation assortment[J].Physics Letters A,2016,380(1/2):40-47.
[11]GUO H,CHU C,SHEN C,et al.Reputation-based coevolution of link weights promotes cooperation in spatial prisoner's dilemma game[J].Chaos,Solitons&Fractals,2018,109:265-268.
[12]ZHANG G Q,HU T P,YU Z.An improved fitness evaluation mechanism with noise in prisoner's dilemma game[J].Applied Mathematics&Computation,2016,276:31-36.
[13]XU X,RONG Z,TSE C K.Bounded rationality optimizes the performance of networked systems in prisoner's dilemma game[C]//ISCAS2018:Proceedings of the 2018 IEEE International Symposium on Circuits and Systems.Piscataway,NJ:IEEE,2018:1-5.
[14]LI Y M,ZHANG J,PERC M.Effects of compassion on the evolution of cooperation in spatial social dilemmas[J].Applied Mathematics and Computation,2018,320:437-443.
[15]GERARDI A,TARDELLI P.Stochastic control methods:hedging in a market described by pure jump processes[J].Acta Applicandae Mathematicae,2010,111(3):233-255.
[16]SZABG,TKE C.Evolutionary prisoner's dilemma game on a square lattice[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,1998,58(1):69-73.
[2]NOWAK M A,MAY R M.Evolutionary games and spatial chaos[J].Nature,1992,359(6398):826-829.
[3]NOWAK M A,MAY R M.The spatial dilemmas of evolution[J].International Journal of Bifurcation and Chaos,1993,3(1):35-78.
[4]WU Z X,RONG Z H,HOLME P.Diversity of reproduction time scale promotes cooperation in spatial prisoner's dilemma games[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,2009,80(3 Pt 2):036106.
[5]RONG Z H,WU Z X,CHEN G R.Coevolution of strategy-selection time scale and cooperation in spatial prisoner's dilemma game[J].Europhysics Letters,2013,102(6):68005.
[6]JIA D Y,JIN J H,DU C P,et al.Effects of inertia on the evolution of cooperation in the voluntary prisoner's dilemma game[J].Physica A:Statistical Mechanics and its Applications,2018,509:817-826.
[7]WU Z X,XU X J,HUANG Z G,et al.Evolutionary prisoner's dilemma game with dynamic preferential selection[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,2006,74(2):021107.
[8]WANG Z,PERC M.Aspiring to the fittest and promotion of cooperation in the prisoner's dilemma game[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,2010,82(2 Pt 1):021115.
[9]XIA C Y,DING S,WANG C J,et al.Risk analysis and enhancement of cooperation yielded by the individual reputation in the spatial public goods game[J].IEEE Systems Journal,2017,11(3):1516-1525.
[10]CHEN M H,WANG L,SUN S W,et al.Evolution of cooperation in the spatial public goods game with adaptive reputation assortment[J].Physics Letters A,2016,380(1/2):40-47.
[11]GUO H,CHU C,SHEN C,et al.Reputation-based coevolution of link weights promotes cooperation in spatial prisoner's dilemma game[J].Chaos,Solitons&Fractals,2018,109:265-268.
[12]ZHANG G Q,HU T P,YU Z.An improved fitness evaluation mechanism with noise in prisoner's dilemma game[J].Applied Mathematics&Computation,2016,276:31-36.
[13]XU X,RONG Z,TSE C K.Bounded rationality optimizes the performance of networked systems in prisoner's dilemma game[C]//ISCAS2018:Proceedings of the 2018 IEEE International Symposium on Circuits and Systems.Piscataway,NJ:IEEE,2018:1-5.
[14]LI Y M,ZHANG J,PERC M.Effects of compassion on the evolution of cooperation in spatial social dilemmas[J].Applied Mathematics and Computation,2018,320:437-443.
[15]GERARDI A,TARDELLI P.Stochastic control methods:hedging in a market described by pure jump processes[J].Acta Applicandae Mathematicae,2010,111(3):233-255.
[16]SZABG,TKE C.Evolutionary prisoner's dilemma game on a square lattice[J].Physical Review E:Statistical,Nonlinear,and Soft Matter Physics,1998,58(1):69-73.