Evolutionary dynamics of cooperation in \(N\)-person snowdrift games with peer punishment and individual disguise. (English) Zbl 07485974
Summary: We introduce individual disguise of non-cooperators into \(N\)-person snowdrift games with peer punishment in a well-mixed population to explore the effects of individual disguise and peer punishment on the cooperation in such games. Firstly, we formulate the reasonable payoffs corresponding to cooperation, non-cooperation and punishment strategy, followed by the establishment of the resulting replicator dynamics to investigate the evolution of the frequencies of the three strategies. Secondly, from a macroscopic perspective, this work provides two-dimensional evolutionary state figures on full cooperation. Moreover, this paper studies the sensitivities of the two-dimensional evolutionary state figures to the third parameter. Specifically, high disguise cost, low cost-to-benefit ratio, severe punishment and large competing size tend to curb non-cooperators and guide the cooperation between cooperators and punishers, which is frozen as non-cooperators vanish. Conversely, low disguise cost, high cost-to-benefit ratio, light punishment and small competing size are disadvantageous to punishers and lead to a continual dynamic with cooperators and non-cooperators, which is a dynamical phase once the punishers disappear. Thirdly, we propose another stochastic evolutionary dynamic for finite but large populations. The corresponding results are in precise agreement with those of the replicator dynamics.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
replicator dynamics; \(N\)-person snowdrift games; individual disguise; peer punishment; mutation-selection processReferences:
| [1] | Rand, D. G.; Nowak, M. A., Human cooperation, Trends Cogn. Sci., 17, 413-425 (2013) |
| [2] | Apicella, C. L.; Silk, J. B., The evolution of human cooperation, Curr. Biol., 29, R447-R450 (2019) |
| [3] | Chen, X.; Sasaki, T.; Perc, M., Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement, Sci. Rep., 5, 17050 (2015) |
| [4] | Kang, K.; Zhao, Y.; Zhang, J.; Qiang, C., Evolutionary game theoretic analysis on low-carbon strategy for supply chain enterprises, J. Cleaner Prod., 230, 981-994 (2019) |
| [5] | Dawes, R. M., Social dilemmas, Annu. Rev. Psychol., 31, 169-193 (1980) |
| [6] | Nowak, M. A., Five rules for the evolution of cooperation, Science, 314, 5805, 1560-1563 (2006) |
| [7] | Perc, M., Phase transitions in models of human cooperation, Phys. Lett. A, 380, 36, 2803-2808 (2016) |
| [8] | Liu, L.; Wang, S.; Chen, X.; Perc, M., Evolutionary dynamics in the public goods games with switching between punishment and exclusion, Chaos, 28, 10, Article 103105 pp. (2018) · Zbl 1457.91077 |
| [9] | Broom, M.; Rychtář, J., Evolutionary games with sequential decisions and dollar auctions, Dyn. Games Appl., 8, 211-231 (2018) · Zbl 1397.91061 |
| [10] | Kokko, H.; López-Sepulcre, A.; Morrell, L. J., From hawks and doves to self-consistent games of territorial behavior, Am. Nat., 167, 6, 901-912 (2006) |
| [11] | Hofbauer, J.; Sigmund, K., Evolutionary Games and Population Dynamics (1998), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0914.90287 |
| [12] | Hofbauer, J.; Sigmund, K., Evolutionary game dynamics, Bull. Amer. Math. Soc., 40, 479-519 (2003) · Zbl 1049.91025 |
| [13] | Nowak, M. A.; Sigmund, K., Evolutionary dynamics of biological games, Science, 303, 5659, 793-799 (2004) |
| [14] | Cressman, R.; Tao, Y., The replicator equation and other game dynamics, Proc. Natl. Acad. Sci. USA, 111, 10810-10817 (2014) · Zbl 1355.91011 |
| [15] | Nesrine, B. K.; Rachid, E. A., Evolutionary games in interacting communities, Dyn. Games Appl., 7, 131-156 (2017) · Zbl 1391.91036 |
| [16] | Hauert, C.; Doebeli, M., Spatial structure often inhibits the evolution of cooperation in the snowdrift game, Nature, 428, 6983, 643 (2004) |
| [17] | Cason, T. N.; Gangadharan, L., Promoting cooperation in nonlinear social dilemmas through peer punishment, Exp. Econ., 18, 66-88 (2015) |
| [18] | Ohdaira, T., Evolution of cooperation by the introduction of the probabilistic peer-punishment based on the difference of payoff, Sci. Rep., 6, 25413 (2016) |
| [19] | Wang, Q.; Liu, L.; Chen, X., Evolutionary dynamics of cooperation in the public goods game with individual disguise and peer punishment, Dyn. Games Appl., 10 (2020) · Zbl 1461.91046 |
| [20] | Xu, M.; Zheng, D. F.; Xu, C.; Zhong, L. X., Cooperative behavior in \(N\)-person evolutionary snowdrift games with punishment, Physica A, 424, 322-329 (2015) · Zbl 1400.91086 |
| [21] | Zhu, P.; Guo, H.; Zhang, H., The role of punishment in the spatial public goods game, Nonlinear Dynam., 102, 6983, 1-10 (2020) |
| [22] | Takesue, H., Evolutionary prisoner’s dilemma games on the network with punishment and opportunistic partner switching, Epl, 121, 4 (2017) |
| [23] | Yang, H. X.; Wang, Z., Role of mutual punishment in the snowdrift game, Europhys. Lett., 111, 6, 60003 (2015) |
| [24] | Sasaki, T.; Unemi, T., Replicator dynamics in public goods games with reward funds, J. Theoret. Biol., 287, 109-114 (2011) · Zbl 1397.91078 |
| [25] | Sasaki, T.; Uchida, S., Rewards and the evolution of cooperation in public good games, Biol. Lett., 10, 1, Article 20130903 pp. (2014) |
| [26] | Wu, Y.; Zhang, B.; Zhang, S., Probabilistic reward or punishment promotes cooperation in evolutionary games, Chaos Solitons Fractals, 103, 289-293 (2017) · Zbl 1376.91035 |
| [27] | Liu, L.; Chen, X.; Szolnoki, A., Competitions between prosocial exclusions and punishments in finite populations, Sci. Rep., 7, 46634 (2017) |
| [28] | Sasaki, T.; Uchida, S., The evolution of cooperation by social exclusion, Proc. R. Soc. B, 280, 1752, Article 20122498 pp. (2013) |
| [29] | Quan, J.; Yang, W.; Li, X.; Wang, X.; Yang, J. B., Social exclusion with dynamic cost on the evolution of cooperation in spatial public goods games, Appl. Math. Comput., 372, Article 124994 pp. (2020) · Zbl 1433.91027 |
| [30] | Cuesta, J. A.; Gracia-lázaro, C.; Ferrer, A.; Moreno, Y., Reputation drives cooperative behaviour and network formation in human groups, Sci. Rep., 5, 7843 (2015) |
| [31] | Ma, Y.; Lu, J.; Shi, L., Diversity of neighborhoods promotes cooperation in evolutionary social dilemmas, Physica A, 468 (2017) · Zbl 1400.91069 |
| [32] | Jin, J.; Chu, C.; Shen, C., Heterogeneous fitness promotes cooperation in the spatial prisoner’s dilemma game, Chaos Solitons Fractals, 106 (2018) · Zbl 1394.91041 |
| [33] | Chen, X., Probabilistic sharing solves the problem of costly punishment, New J. Phys., 16, Article 083016 pp. (2014) |
| [34] | Chen, X., Competition and cooperation among different punishing strategies in the spatial public goods game, Phys. Rev. E, 92, Article 012819 pp. (2015) |
| [35] | Zheng, D. F.; Yin, H. P.; Chan, C. H.; Hui, P. M., Cooperative behavior in a model of evolutionary snowdrift games with N-person interactions, Epl, 80, 1, 417-429 (2008) |
| [36] | Lee, K. H.; Chan, C. H.; Hui, P. M., Cooperation in N-person evolutionary snowdrift game in scale-free Barabási-Albert networks, Physica A, 387, 22, 5602-5608 (2008) |
| [37] | Souza, M. O.; Pacheco, J. M.; Santos, F. C., Evolution of cooperation under N-person snowdrift games, J. Theoret. Biol., 260, 4, 581-588 (2009) · Zbl 1402.91061 |
| [38] | Ji, M.; Xu, C.; Hui, P. M., Effects of dynamical grouping on cooperation in N-person evolutionary snowdrift game, Phys. Rev. E, 84, 3, 36113 (2011) |
| [39] | Sui, X.; Cong, R.; Li, K.; Wang, L., Evolutionary dynamics of N-person snowdrift game, Phys. Lett. A, 379, 45-46, 2922-2934 (2015) · Zbl 1349.91046 |
| [40] | Xu, M.; Zheng, D. F.; Xu, C.; Hui, P. M., Three-strategy N-person snowdrift game incorporating loners, Physica A, 468 (2016) · Zbl 1400.91085 |
| [41] | Wettergren, T. A., Replicator dynamics of an N-player snowdrift game with delayed payoffs, Appl. Math. Comput., 404, 1, Article 126204 pp. (2021) · Zbl 1510.91041 |
| [42] | Shu, F.; Liu, X.; Fang, K.; Chen, H., Memory-based snowdrift game on a square lattice, Physica A, 15-26 (2018) |
| [43] | Bayer, P.; Brown, J. S.; Staňková, K., A two-phenotype model of immune evasion by cancer cells, J. Theoret. Biol., 455, 191-204 (2018) · Zbl 1406.92142 |
| [44] | Liu, L.; Chen, X.; Szolnoki, A., Evolutionary dynamics of cooperation in a population with probabilistic corrupt enforcers and violators, Math. Models Methods Appl. Sci., 29, 11, 2127-2149 (2019) · Zbl 1428.91005 |
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