Cooperation driven by mutations in multi-person Prisoner's Dilemma

Abstract

The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoner's Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that time-scale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterized by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterized by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size. For some parameter values, we find more than one stable fixed point, corresponding to different structures of the initial population.

Exploration dynamics in evolutionary games

“…Here, we focus on the effect of random exploration and demonstrate that the mutation rate can trigger qualitative changes in the evolutionary dynamics (26)(27)(28)(29)(30). To illustrate how increasing mutation probabilities affect the evolutionary dynamics, we address the evolution of cooperation and punishment in Nplayer public goods games in finite populations.…”

The dependency game: Multiperson reciprocal sharing leads to stable cooperation which can evolve into group formation

“…This is in contrast to other (multiperson) PDs, which only have options C or D (Eriksson and Lindgren, 2005). In the 3-person dependency game, this results in 27 different possible outcomes ((X|Y|Z), with X,Y,Z ∈{D,CL,CR}) ( Table 2).…”

“…In the classic interpretation of the PD, two players act simultaneously, after which a payoff follows, and this simultaneousness has been retained in multiperson PD games (Boyd and Richerson, 1988;Eriksson and Lindgren, 2005; and references therein). A good example of a simultaneous collaboration is a dyke building project, because all members make their contributions and harvest at the same time.…”

Study on Cooperative Mechanism of Prefabricated Producers Based on Evolutionary Game Theory

“…Yang and PeiHua [4] analyzed the dynamic evolution factors affecting the cooperation or competition mechanism between producers and suppliers in the supply chain through evolutionary game theory, including the initial proportion of the game subject, distribution of benefits, initial investment cost, and discount factor. Eriksson and Lindgren [5] discussed the effect of the game population scale, value of the income parameter, structure of initial scale, and mutation rate on the evolutionary process after analyzing the mechanism of mutation on cooperation, using the prisoner's dilemma model. Based on the analysis of evolution path and the influencing factors of horizontal enterprises, Su et al [6] find that the growth of clusters promotes cooperative network formation, especially among small and medium-sized enterprises.…”