Evolution of donations on scale-free networks during a COVID-19 breakout

doi:10.1088/1674-1056/ac4651

中国物理B ›› 2022, Vol. 31 ›› Issue (8): 80204-080204.doi: 10.1088/1674-1056/ac4651

Evolution of donations on scale-free networks during a COVID-19 breakout

Xian-Jia Wang(王先甲)^1,2 and Lin-Lin Wang(王琳琳)^1,†

1 Economics and Management School, Wuhan University, Wuhan 430072, China;
2 Institute of Systems Engineering, Wuhan University, Wuhan 430072, China

收稿日期:2021-10-12 修回日期:2021-12-13 接受日期:2021-12-24 出版日期:2022-07-18 发布日期:2022-07-27
通讯作者: Lin-Lin Wang E-mail:2015301580305@whu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 72031009 and 71871171) and the National Social Science Foundation of China (Grant No. 20&ZD058).

Evolution of donations on scale-free networks during a COVID-19 breakout

Xian-Jia Wang(王先甲)^1,2 and Lin-Lin Wang(王琳琳)^1,†

1 Economics and Management School, Wuhan University, Wuhan 430072, China;
2 Institute of Systems Engineering, Wuhan University, Wuhan 430072, China

Received:2021-10-12 Revised:2021-12-13 Accepted:2021-12-24 Online:2022-07-18 Published:2022-07-27
Contact: Lin-Lin Wang E-mail:2015301580305@whu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 72031009 and 71871171) and the National Social Science Foundation of China (Grant No. 20&ZD058).

摘要/Abstract

摘要： Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield for donors, and it has the characteristics of the prisoners' dilemma. This paper discusses why timely donations in the early stages of COVID-19 occurred. Based on the idea that donation is a strategy adopted by players during interconnection on account of their understanding of the environment, donation-related populations are placed on social networks and the inter-correlation structures in the population are described by scale-free networks. Players in donation-related populations are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi update rule, whereas the conversion between legal beneficiaries and the other three types is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters of the utility function, the noise intensity, the utility coefficient, the donation coefficient and the initial states of the population on the scale-free network change. For population sizes of 50, 100, 150, and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation and study the corresponding steady states and structural characteristics of the population. We identify the best ranges of the noise intensity K, the donation coefficient α and the utility coefficient β for promoting cooperation at different population sizes. Furthermore, with the increase of the population size, the donor traps are found. At the same time, it is discovered that the initial states of the population have a great impact on the steady states; thus the upper and lower triangle phenomena are proposed. We also find that the population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.

关键词: donation, public goods game, evolutionary game, scale-free network

Abstract: Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield for donors, and it has the characteristics of the prisoners' dilemma. This paper discusses why timely donations in the early stages of COVID-19 occurred. Based on the idea that donation is a strategy adopted by players during interconnection on account of their understanding of the environment, donation-related populations are placed on social networks and the inter-correlation structures in the population are described by scale-free networks. Players in donation-related populations are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi update rule, whereas the conversion between legal beneficiaries and the other three types is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters of the utility function, the noise intensity, the utility coefficient, the donation coefficient and the initial states of the population on the scale-free network change. For population sizes of 50, 100, 150, and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation and study the corresponding steady states and structural characteristics of the population. We identify the best ranges of the noise intensity K, the donation coefficient α and the utility coefficient β for promoting cooperation at different population sizes. Furthermore, with the increase of the population size, the donor traps are found. At the same time, it is discovered that the initial states of the population have a great impact on the steady states; thus the upper and lower triangle phenomena are proposed. We also find that the population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.

Key words: donation, public goods game, evolutionary game, scale-free network

中图分类号: (Decision theory and game theory)

02.50.Le

05.45.Pq (Numerical simulations of chaotic systems)

Xian-Jia Wang(王先甲) and Lin-Lin Wang(王琳琳). Evolution of donations on scale-free networks during a COVID-19 breakout[J]. 中国物理B, 2022, 31(8): 80204-080204.

Xian-Jia Wang(王先甲) and Lin-Lin Wang(王琳琳). Evolution of donations on scale-free networks during a COVID-19 breakout[J]. Chin. Phys. B, 2022, 31(8): 80204-080204.

参考文献

[1] Hauert C, De Monte S and Hofbauer J 2002 J. Theor. Biol. 218 187
[2] Nowak M A and Sigmund K 2005 Nature 437 1291
[3] Balliet D, Mulder L B and Van Lange P A M 2011 Psychol. Bull. 137 594
[4] Alexander R D 1974 Annu. Rev. Ecol. Syst. 5 325
[5] Press W H and Dyson F J 2012 Proc. Natl. Acad. Sci. USA 109 10409
[6] Ohtsuki H, Hauert C, Lieberman E and Nowak M A 2006 Nature 441 502
[7] Nowak M A and May R M 1992 Nature 359 826
[8] Perc M 2009 New J. Phys. 11 033027
[9] Amaral M A, Wardil L, Perc M and da Silva J K L 2016 Phys. Rev. E. 93 042304
[10] Barabási A L and Oltvai Z N 2004 Nat. Rev. Genet. 5 101
[11] Yoshimura J and Jansen V A A 1996 Popul. Ecol. 38 165
[12] Zhang B Y, Li C and Tao Y 2016 Dyn. Games Appl. 6 567
[13] Li Y M, Du W B, Yang P, Wu T H, Wu D P and Perc M 2019 IEEE Internet Things J. 6 1866
[14] Bu Z, Li H J, Zhang C, Cao J, Li A and Shi Y 2020 IEEE T. Knowl Data En. 32 1348
[15] Daskalakis C, Goldberg P W and Papadimitriou C H 2009 Commun. ACM 52 89
[16] Dong Y, Ma S, Zhang B, Wang W X and Pacheco J M 2021 One Earth 4 1141
[17] Santos F C, Santos M D and Pacheco J M 2008 Nature 454 213
[18] Dawes R M, Orbell J M, Simmons R T and Alphons J C V 1986 Am. Polit. Sci. Rev. 80 1171
[19] Bagnoli M and Lipman B L 1989 Rev. Econ. Stud. 56 583
[20] Chaudhuri A 2011 Exp. Econ. 14 47
[21] Wilkinson G S 1984 Nature 308 181
[22] Valerio C 2015 Sci. Rep. 5 9916
[23] Wang Z, Jusup M, Wang R W, Shi L, Iwasa Y, Moreno Y and Kurths J 2017 Sci. Adv. 3 1601444
[24] Li H J, Bu Z, Wang Z and Cao J 2020 IEEE T. Ind. Inform. 16 5327
[25] Tran C, Shin W-Y and Spitz A 2022 ACM T. Knowl. Discov. D. 16 1
[26] Li H J, Bu Z, Wang Z, Pei J, Cao J and Shi Y 2022 IEEE T. Knowl. Data En. 34 2860
[27] Barabasi A L and Albert R 1999 Science 286 509
[28] Li H J, Wang L, Zhang Y and Perc M 2020 New J. Phys. 22 063035
[29] Li H J, Xu W Z, Song S P, Wang W X and Perc M 2021 Chaos Soliton. Fract. 151 111294
[30] Holme P and Kim B J 2002 Phys. Rev. E 65 026107
[31] Broido A D and Clauset A 2019 Nat. Commun. 10 1017
[32] Kleineberg K K 2017 Nat. Commun. 8 1888
[33] Santos F C, Rodrigues J F and Pacheco J M 2005 Phys. Rev. E 72 056128
[34] Gomez-Gardenes J, Campillo M, Fiona L M and Moreno Y 2007 Phys. Rev. Lett. 98 108103
[35] Perc M and Szolnoki A 2008 Phys. Rev. E 77 011904
[36] Rong Z and Wu Z X 2009 Europhys. Lett. 87 30001
[37] Xu X, Rong Z, Wu Z X, Zhou T and Tse C K 2017 Phys. Rev. E 95 052302
[38] Assenza S, Gómez-Gardeñes J and Latora V 2008 Phys. Rev. E 78 017101
[39] Du W B, Cao X B, Hu M B and Wang X J 2009 Epl 87 60004
[40] Li Y, Zhang J and Perc M 2018 Appl. Math. Comput. 320 437
[41] Brandt H and Sigmund K 2005 P Natl. Acad. Sci. USA. 102 2666
[42] Wang Z, Xu Z J and Zhang L Z 2010 Chin. Phys. B 19 110201
[43] Szolnoki A and Perc M 2010 Europhys. Lett. 92 38003
[44] Di S, Xiang Y and Zhao P 2022 B Iran. Math. Soc. 48 849
[45] Jiang C, Guo D and Xu R 2021 Appl. Intell. 51 1
[46] Szolnoki A, Perc M and Szabó G 2009 Phys. Rev. E 80 056109
[47] Szolnoki A and Danku Z 2018 Physica A 511 371
[48] Szolnoki A and Chen X 2017 Europhys. Lett. 120 58001
[49] Perc M 2016 Phys. Lett. A 380 2803
[50] Perc M 2011 New J. Phys. 13 123027
[51] Perc M, Gómez-Gardeñes J, Szolnoki A, Floría L M and Moreno Y 2013 J. R. Soc. Interface 10 20120997

Evolution of donations on scale-free networks during a COVID-19 breakout

Evolution of donations on scale-free networks during a COVID-19 breakout

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Jinming Du(杜金铭). Voter model on adaptive networks[J]. 中国物理B, 2022, 31(5): 58902-058902.
[2]	Jian-Wei Wang(王建伟), Rong Wang(王蓉), and Feng-Yuan Yu(于逢源). Fitness of others' evaluation effect promotes cooperation in spatial public goods game[J]. 中国物理B, 2021, 30(12): 128701-128701.
[3]	苏桂锋, 李晓温, 张小兵, 张一. Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks[J]. 中国物理B, 2020, 29(8): 88904-088904.
[4]	王先甲, 陈文嫚. The evolution of cooperation in public good game with deposit[J]. 中国物理B, 2019, 28(8): 80201-080201.
[5]	王先甲, 顾翠伶, 吕少杰, 全吉. Evolutionary game dynamics of combining the Moran and imitation processes[J]. 中国物理B, 2019, 28(2): 20203-020203.
[6]	全吉, 储育青, 刘伟, 王先甲, 阳修康. Stochastic evolutionary public goods game with first and second order costly punishments in finite populations[J]. 中国物理B, 2018, 27(6): 60203-060203.
[7]	孟庆宽, 冯东太, 孙玉萍, 周爱萍, 孙艳, 谭树刚, 高绪团. Study on the phase transition of the fractal scale-free networks[J]. 中国物理B, 2018, 27(10): 106402-106402.
[8]	濮存来, 李杰, 陈荣斌, 许忠奇. Multiple-predators-based capture process on complex networks[J]. 中国物理B, 2017, 26(3): 38901-038901.
[9]	王宝英, 龚玉兵. Effects of channel noise on synchronization transitions in delayed scale-free network of stochastic Hodgkin-Huxley neurons[J]. 中国物理B, 2015, 24(11): 118702-118702.
[10]	郭进利. Co-evolution of the brand effect and competitiveness in evolving networks[J]. , 2014, 23(7): 70206-070206.
[11]	盘薇, 薛郁, 赵瑞, 卢伟真. Biham-Middleton-Levine model in consideration of cooperative willingness[J]. 中国物理B, 2014, 23(5): 58902-058902.
[12]	艾均, 赵海, Kathleen M. Carleyb, 苏湛, 李辉. Evolution of IPv6 Internet topology with unusual sudden changes[J]. 中国物理B, 2013, 22(7): 78902-078902.
[13]	华达银. Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model[J]. Chin. Phys. B, 2013, 22(4): 40512-040512.
[14]	凌翔, 胡茂彬, 丁建勋. Effects of node buffer and capacity on network traffic[J]. 中国物理B, 2012, 21(9): 98902-098902.
[15]	方祥圣, 朱平, 刘润然, 刘恩钰, 魏贵义. A 2-stage strategy updating rule promotes cooperation in the prisoner's dilemma game[J]. 中国物理B, 2012, 21(10): 108702-108702.