Skip to main content
Log in

Social dynamics and Parrondo’s paradox: a narrative review

  • Review
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

How do group dynamics affect individuals within the group? How do individuals, in turn, affect group dynamics? As society comes together, individuals affect the group dynamics and vice versa. Social dynamics look at group dynamics, its effect on individuals, conformity, leadership, networks, and more. In the past two decades, the game theoretic Parrondo’s paradox has been used to model and explain the different aspects of social dynamics. Two losing games can be combined in a certain manner to give a winning outcome—this is known as Parrondo’s paradox. In this review, the connections between Parrondo’s paradox and social dynamics are discussed with emphasis on (i) cooperation and competition, (ii) resource redistribution and social welfare, and (iii) information flow and decision-making.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Gittler, J.B.: Social Dynamics: Principles and Cases in Introductory Sociology. McGraw-Hill, London (1952)

    Google Scholar 

  2. Young, H.P.: Social dynamics: theory and applications. Handb. Comput. Econ. 2, 1081–1108 (2006)

    Google Scholar 

  3. Durlauf, S.N., Young, H.P.: Social Dynamics, vol. 4. MIT Press, London (2004)

    MATH  Google Scholar 

  4. Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591 (2009)

    Google Scholar 

  5. Perc, M., Gómez-Gardeñes, J., Szolnoki, A., Floría, L.M., Moreno, Y.: Evolutionary dynamics of group interactions on structured populations: a review. J. R. Soc. Interface 10, 20120997 (2013)

    Google Scholar 

  6. Tuma, N.B.: Social Dynamics Models and Methods. Elsevier, London (1984)

    Google Scholar 

  7. Von Neumann, J., Morgenstern, O.: Theory of games and economic behavior. Bull. Am. Math. Soc. 51, 498–504 (1945)

    MathSciNet  Google Scholar 

  8. Nash, J.: Non-cooperative games. Ann. Math. 54, 286–295 (1951)

    MathSciNet  MATH  Google Scholar 

  9. Schelling, T.C.: The strategy of conflict. Prospectus for a reorientation of game theory. J. Confl. Resolut. 2, 203–264 (1958)

    Google Scholar 

  10. Bousquet, F., Lifran, R., Tidball, M., Thoyer, S., Antona, M.: Agent-based modelling, game theory and natural resource management issues. J. Artif. Soc. Soc. Simul. 4, 637–650 (2001)

    Google Scholar 

  11. Swedberg, R., Augier, M.: Game theory and sociology: landmarks in game theory from a sociological perspective. Hist. Econ. Ideas 11, 15–42 (2003)

    Google Scholar 

  12. Khan, S.U., Ahmad, I.: Non-cooperative, semi-cooperative, and cooperative games-based grid resource allocation. In: Proceedings 20th IEEE International Parallel and Distributed Processing Symposium, p. 10. IEEE, New York (2006)

  13. Çolak, S., Lima, A., González, M.C.: Understanding congested travel in urban areas. Nat. Commun. 7, 10793 (2016)

    Google Scholar 

  14. Harmer, G.P., Abbott, D.: Game theory: losing strategies can win by Parrondo’s paradox. Nature 402, 864 (1999)

    Google Scholar 

  15. Harmer, G.P., Abbott, D., Taylor, P.G., Parrondo, J.M.: Parrondo’s paradoxical games and the discrete Brownian ratchet. In: AIP Conference Proceedings, vol. 511, pp. 189–200. AIP, London (2000)

  16. Pearce, C.E.: Entropy, Markov information sources and Parrondo games. In: AIP Conference Proceedings, vol. 511, pp. 207–212. AIP, London (2000)

  17. Soo, W.W.M., Cheong, K.H.: Parrondo’s paradox and complementary Parrondo processes. Physica A 392, 17–26 (2013)

    MathSciNet  Google Scholar 

  18. Soo, W.W.M., Cheong, K.H.: Occurrence of complementary processes in Parrondo’s paradox. Physica A 412, 180–185 (2014)

    MathSciNet  MATH  Google Scholar 

  19. Cheong, K.H., Soo, W.W.M.: Construction of novel stochastic matrices for analysis of Parrondo’s paradox. Physica A 392, 4727–4738 (2013)

    MathSciNet  MATH  Google Scholar 

  20. Cheong, K.H., Saakian, D.B., Zadourian, R.: Allison mixture and the two-envelope problem. Phys. Rev. E 96, 062303 (2017)

    Google Scholar 

  21. Cheong, K.H., et al.: Paradoxical simulations to enhance education in mathematics. IEEE Access 7, 17941–17950 (2019)

    Google Scholar 

  22. Jia, S., Lai, J.W., Koh, J.M., Xie, N.G., Cheong, K.H.: Parrondo effect: exploring the nature-inspired framework on periodic functions. Physica A 556, 124714 (2020). https://doi.org/10.1016/j.physa.2020.124714

    Article  Google Scholar 

  23. Rajendran, J., Benjamin, C.: Playing a true Parrondo’s game with a three-state coin on a quantum walk. EPL 122, 40004 (2018)

    Google Scholar 

  24. Rajendran, J., Benjamin, C.: Implementing Parrondo’s paradox with two-coin quantum walks. R. Soc. Open Sci. 5, 171599 (2018)

    Google Scholar 

  25. Lai, J.W., Cheong, K.H.: Parrondo’s paradox from classical to quantum: a review. Nonlinear Dyn. 100, 849–861 (2020)

    MATH  Google Scholar 

  26. Lai, J.W., Cheong, K.H.: Parrondo effect in quantum coin-toss simulations. Phys. Rev. E 101, 052212 (2020)

    Google Scholar 

  27. Osipovitch, D.C., Barratt, C., Schwartz, P.M.: Systems chemistry and Parrondo’s paradox: computational models of thermal cycling. New J. Chem. 33, 2022–2027 (2009)

    Google Scholar 

  28. Allison, A., Abbott, D.: Control systems with stochastic feedback. Chaos 11, 715–724 (2001)

    MATH  Google Scholar 

  29. Chang, C.-H., Tsong, T.Y.: Truncation and reset process on the dynamics of Parrondo’s games. Phys. Rev. E 67, 025101 (2003)

    Google Scholar 

  30. Kocarev, L., Tasev, Z.: Lyapunov exponents, noise-induced synchronization, and Parrondo’s paradox. Phys. Rev. E 65, 046215 (2002)

    MathSciNet  MATH  Google Scholar 

  31. Cheong, K.H., Koh, J.M.: A hybrid genetic-Levenberg–Marquardt algorithm for automated spectrometer design optimization. Ultramicroscopy 202, 100–106 (2019)

    Google Scholar 

  32. Koh, J.M., Cheong, K.H.: Automated electron-optical system optimization through switching Levenberg–Marquardt algorithms. J. Electron Spectrosc. Relat. Phenom. 227, 31–39 (2018)

    Google Scholar 

  33. Reed, F.A.: Two-locus epistasis with sexually antagonistic selection: a genetic Parrondo’s paradox. Genetics 176, 1923–1929 (2007)

    Google Scholar 

  34. Ye, Y., Xie, N.-G., Wang, L.-G., Meng, R., Cen, Y.-W.: Study of biotic evolutionary mechanisms based on the multi-agent Parrondo’s games. Fluct. Noise Lett. 11, 1250012 (2012)

    Google Scholar 

  35. Cheong, K.H., Tan, Z.X., Xie, N.-G., Jones, M.C.: A paradoxical evolutionary mechanism in stochastically switching environments. Sci. Rep. 6, 34889 (2016)

    Google Scholar 

  36. Tan, Z.X., Cheong, K.H.: Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction. eLife 6, e21673 (2017)

    Google Scholar 

  37. Koh, J.M., Xie, N.-G., Cheong, K.H.: Nomadic-colonial switching with stochastic noise: subsidence-recovery cycles and long-term growth. Nonlinear Dyn. 94, 1467–1477 (2018)

    Google Scholar 

  38. Cheong, K.H., Koh, J.M., Jones, M.C.: Multicellular survival as a consequence of Parrondo’s paradox. Proc. Natl. Acad. Sci. 115, E5258–E5259 (2018)

    Google Scholar 

  39. Cheong, K.H., Koh, J.M., Jones, M.C.: Paradoxical survival: examining the Parrondo effect across biology. BioEssays 41, 1900027 (2019)

    Google Scholar 

  40. Cheong, K.H., Koh, J.M., Jones, M.C.: Do arctic hares play Parrondo’s games? Fluct. Noise Lett. 18, 1971001 (2019)

    Google Scholar 

  41. Tan, Z.-X., Koh, J.M., Koonin, E.V., Cheong, K.H.: Predator dormancy is a stable adaptive strategy due to Parrondo’s paradox. Adv. Sci. 7, 1901559 (2020)

    Google Scholar 

  42. Tan, Z.-X., Cheong, K.H.: Periodic habitat destruction and migration can paradoxically enable sustainable territorial expansion. Nonlinear Dyn. 98, 1–13 (2019)

    MATH  Google Scholar 

  43. Ye, Y., et al.: Ratcheting based on neighboring niches determines lifestyle. Nonlinear Dyn. 98, 1821–1830 (2019)

    MATH  Google Scholar 

  44. Comte, A.: System of Positive Polity: Social Dynamics; or, the General Theory of Human Progress, vol. 3. Longmans, Green and Company, London (1876)

    Google Scholar 

  45. Harmer, G.P., Abbott, D.: Parrondo’s paradox. Stat. Sci. 14, 206–213 (1999)

    MathSciNet  MATH  Google Scholar 

  46. Harmer, G.P., Abbott, D.: A review of Parrondo’s paradox. Fluct. Noise Lett. 2, R71–R107 (2002)

    Google Scholar 

  47. Parrondo, J.M., Harmer, G.P., Abbott, D.: New paradoxical games based on Brownian ratchets. Phys. Rev. Lett. 85, 5226 (2000)

    Google Scholar 

  48. Harmer, G.P., Abbott, D., Parrondo, J.M.: Parrondo’s capital and history-dependent games. In: Nowak, A.S., Szajowski, K. (eds.) Advances in Dynamic Games, pp. 635–648. Springer, Basel, Switzerland (2005)

    MATH  Google Scholar 

  49. Toral, R.: Cooperative Parrondo’s games. Fluct. Noise Lett. 1, L7–L12 (2001)

    MathSciNet  Google Scholar 

  50. Dinis, L., Parrondo, J.M.: Optimal strategies in collective Parrondo games. EPL 63, 319 (2003)

    Google Scholar 

  51. Amengual, P., Meurs, P., Cleuren, B., Toral, R.: Reversals of chance in paradoxical games. Physica A 371, 641–648 (2006)

    Google Scholar 

  52. Xie, N.-G., et al.: Theoretical analysis and numerical simulation of Parrondo’s paradox game in space. Chaos Solitons Fractals 44, 401–414 (2011)

    MathSciNet  MATH  Google Scholar 

  53. Ethier, S., Lee, J.: Parrondo games with spatial dependence. Fluct. Noise Lett. 11, 1250004 (2012)

    Google Scholar 

  54. Ethier, S., Lee, J.: Parrondo games with spatial dependence, II. Fluct. Noise Lett. 11, 1250030 (2012)

    Google Scholar 

  55. Li, Y.-F., et al.: A new theoretical analysis approach for a multi-agent spatial Parrondo’s game. Physica A 407, 369–379 (2014)

    MathSciNet  MATH  Google Scholar 

  56. Ethier, S.N., Lee, J.: Parrondo games with spatial dependence, III. Fluct. Noise Lett. 14, 1550039 (2015)

    Google Scholar 

  57. Ethier, S., Lee, J.: Parrondo games with two-dimensional spatial dependence. Fluct. Noise Lett. 16, 1750005 (2017)

    Google Scholar 

  58. Ejlali, N., Pezeshk, H., Chaubey, Y.P., Sadeghi, M.: Parrondo’s paradox for games with three players. Technical Report. Concordia University (2018)

  59. Mihailović, M., Zoranand, R.: One dimensional asynchronous cooperative Parrondo’s games. Fluct. Noise Lett. 3, L389–L398 (2003)

    MathSciNet  Google Scholar 

  60. Mihailović, Z., Rajković, M.: Cooperative Parrondo’s games on a two-dimensional lattice. Physica A 365, 244–251 (2006)

    Google Scholar 

  61. Mihailović, Z., Rajković, M.: Synchronous cooperative Parrondo’s games. Fluct. Noise Lett. 3, L399–L406 (2003)

    MathSciNet  Google Scholar 

  62. Perc, M.: Phase transitions in models of human cooperation. Phys. Lett. A 380, 2803–2808 (2016)

    Google Scholar 

  63. Perc, M., et al.: Statistical physics of human cooperation. Phys. Rep. 687, 1–51 (2017)

    MathSciNet  MATH  Google Scholar 

  64. Wang, L.-G., et al.: Game-model research on coopetition behavior of Parrondo’s paradox based on network. Fluct. Noise Lett. 10, 77–91 (2011)

    Google Scholar 

  65. Ye, Y., Xie, N.-G., Wang, L.-G., Wang, L., Cen, Y.-W.: Cooperation and competition in history-dependent Parrondo’s game on networks. Fluct. Noise Lett. 10, 323–336 (2011)

    Google Scholar 

  66. Ye, Y., Cheong, K.H., Cen, Y.-W., Xie, N.-G.: Effects of behavioral patterns and network topology structures on Parrondo’s paradox. Sci. Rep. 6, 37028 (2016)

    Google Scholar 

  67. Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47 (2002)

    MathSciNet  MATH  Google Scholar 

  68. Arizmendi, C.: Paradoxical way for losers in a dating game. In: AIP Conference Proceedings, vol. 913, pp. 20–25. AIP, London (2007)

  69. Amengual, P., Toral, R.: Truels, or survival of the weakest. Comput. Sci. Eng. 8, 88 (2006)

    Google Scholar 

  70. Zhang, Y.-C.: Happier world with more information. Physica A 299, 104–120 (2001)

    MATH  Google Scholar 

  71. Laureti, P., Zhang, Y.-C.: Matching games with partial information. Physica A 324, 49–65 (2003)

    MathSciNet  MATH  Google Scholar 

  72. Rastegari, B., Condon, A., Immorlica, N., Leyton-Brown, K.: Two-sided matching with partial information. In: Proceedings of the 14th ACM Conference on Electronic Commerce, pp. 733–750 (2013)

  73. Roca, C.P., Cuesta, J.A., Sánchez, A.: Imperfect imitation can enhance cooperation. EPL 87, 48005 (2009)

    Google Scholar 

  74. Bar-Yam, Y., Langlois-Meurinne, J., Kawakatsu, M., Garcia, R.: Preliminary steps toward a universal economic dynamics for monetary and fiscal policy. Preprint arXiv:1710.06285 (2017)

  75. Bar-Yam, Y.: Steering the economy toward growth. Technical Report. New England Complex Systems Institute (2017)

  76. Toral, R.: Capital redistribution brings wealth by Parrondo’s paradox. Fluct. Noise Lett. 2, L305–L311 (2002)

    MathSciNet  Google Scholar 

  77. Zappala, D.A., Pluchino, A., Rapisarda, A.: Selective altruism in collective games. Physica A 410, 496–512 (2014)

    MathSciNet  MATH  Google Scholar 

  78. Helbing, D.: Economics 2.0: the natural step towards a self-regulating, participatory market society. Evol. Inst. Econ. Rev. 10, 3–41 (2013)

    Google Scholar 

  79. Koh, J.M., Cheong, K.H.: New doubly-anomalous Parrondo’s games suggest emergent sustainability and inequality. Nonlinear Dyn. 96, 257–266 (2019)

    Google Scholar 

  80. Koh, J.M., Cheong, K.H.: Emergent preeminence of selfishness: an anomalous Parrondo perspective. Nonlinear Dyn. 98, 943–951 (2019)

    Google Scholar 

  81. Ye, Y., et al.: Passive network evolution promotes group welfare in complex networks. Chaos Solitons Fractals 130, 109464 (2020)

    MathSciNet  Google Scholar 

  82. Farooqui, A.D., Niazi, M.A.: Game theory models for communication between agents: a review. Complex Adapt. Syst. Model. 4, 13 (2016)

    Google Scholar 

  83. Albrecht, S., Lübcke, M., Malsch, T., Schlieder, C.: Scalability and the social dynamics of communication. on comparing social network analysis and communication-oriented modelling as models of communication networks. In: Fischer, K., Florian, M., Malsch, T. (eds.) Socionics, pp. 242–262. Springer, Berlin (2005)

  84. Dinís, L., Parrondo, J.M.: Inefficiency of voting in Parrondo games. Physica A 343, 701–711 (2004)

    MathSciNet  Google Scholar 

  85. Parrondo, J.M., Dinis, L., García-Toraño, E., Sotillo, B.: Collective decision making and paradoxical games. Eur. Phys. J. Spec. Top. 143, 39–46 (2007)

    Google Scholar 

  86. Xie, N.-G., Guo, J.-Y., Ye, Y., Wang, C., Wang, L.: The paradox of group behaviors based on Parrondo’s games. Physica A 391, 6146–6155 (2012)

    Google Scholar 

  87. Ma, H.F., Cheung, K.W., Lui, G.C., Wu, D., Szeto, K.Y.: Effect of information exchange in a social network on investment. Comput. Econ. 54, 1491–1503 (2019)

    Google Scholar 

  88. Dong, Y., Ding, Z., Martínez, L., Herrera, F.: Managing consensus based on leadership in opinion dynamics. Inf. Sci. 397, 187–205 (2017)

    MATH  Google Scholar 

  89. Wang, C., et al.: A rumor spreading model based on information entropy. Sci. Rep. 7, 9615 (2017)

    Google Scholar 

  90. Tan, Z.X., Cheong, K.H.: Cross-issue solidarity and truth convergence in opinion dynamics. J. Phys. A: Math. Theor. 51, 355101 (2018)

    MathSciNet  MATH  Google Scholar 

  91. Wang, C., Koh, J.M., Cheong, K.H., Xie, N.-G.: Progressive information polarization in a complex-network entropic social dynamics model. IEEE Access 7, 35394–35404 (2019)

    Google Scholar 

  92. Dong, Y., Zhan, M., Kou, G., Ding, Z., Liang, H.: A survey on the fusion process in opinion dynamics. Inf. Fusion 43, 57–65 (2018)

    Google Scholar 

  93. Li, K., Liang, H., Kou, G., Dong, Y.: Opinion dynamics model based on the cognitive dissonance: an agent-based simulation. Inf. Fusion 56, 1–14 (2020)

    Google Scholar 

  94. Recuero, R., Zago, G., Soares, F.: Using Social Network Analysis and Social Capital to Identify User Roles on Polarized Political Conversations on Twitter, vol. 5, p. 2056305119848745. Social Media + Society, Berlin (2019)

  95. Al-Khateeb, S., Hussain, M.N., Agarwal, N.: Leveraging social network analysis and cyber forensics approaches to study cyber propaganda campaigns. In: Özyer, T., Bakshi, S., Alhajj, R. (eds.) Social Networks and Surveillance for Society, pp. 19–42. Springer, Cham (2019)

  96. Ning, Y.-Z., Liu, X., Cheng, H.-M., Zhang, Z.-Y.: Effects of social network structures and behavioral responses on the spread of infectious diseases. Physica A 539, 122907 (2020)

    Google Scholar 

  97. Zhang, J., Centola, D.: Social networks and health: new developments in diffusion, online and offline. Annu. Rev. Sociol. 45, 91–109 (2019)

    Google Scholar 

  98. Himelboim, I., Xiao, X., Lee, D.K.L., Wang, M.Y., Borah, P.: A social networks approach to understanding vaccine conversations on Twitter: network clusters, sentiment, and certainty in HPV social networks. Health Commun. 35, 1–9 (2019)

    Google Scholar 

  99. Wei, Y., Lin, Y., Wu, B.: Vaccination dilemma on an evolving social network. J. Theor. Biol. 483, 109978 (2019)

    MathSciNet  MATH  Google Scholar 

  100. Brunson, E.K.: The impact of social networks on parents’ vaccination decisions. Pediatrics 131, e1397–e1404 (2013)

    Google Scholar 

  101. Ising, E.: Beitrag zur theorie des ferromagnetismus. Z. Phys. 31, 253–258 (1925)

    MATH  Google Scholar 

  102. Taroni, A.: Statistical physics: 90 years of the Ising model. Nat. Phys. 11, 997–997 (2015)

    Google Scholar 

Download references

Acknowledgements

This project was funded by the Singapore University of Technology and Design Start-up Research Grant (SRG SCI 2019 142).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kang Hao Cheong.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lai, J.W., Cheong, K.H. Social dynamics and Parrondo’s paradox: a narrative review. Nonlinear Dyn 101, 1–20 (2020). https://doi.org/10.1007/s11071-020-05738-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05738-9

Keywords

Navigation