Advertisement

New doubly-anomalous Parrondo’s games suggest emergent sustainability and inequality

  • Jin Ming Koh
  • Kang Hao CheongEmail author
Original Paper
  • 33 Downloads

Abstract

Parrondo’s games to date have largely focused on the dynamics of capital mean, and not capital spread—the potential of the framework in modelling ecological and socioeconomic sustainability and inequality has thus been ignored. Based on behavioural heuristics of distinct individualistic and multipartite interactive strategies, we introduce a novel multi-agent Parrondo game structure with dynamics dependent upon local inequality. Intriguingly, we observe the presence of doubly-anomalous scenarios, in which there is paradoxical population growth despite both pure strategies being losing, simultaneously accompanied by a suppression of inter-population capital variance to within constant bounds. Ecologically, this reflects sustainable population proliferation amidst disadvantageous conditions; the converse scenario in turn corresponds to inequality-plagued unsustainable growth. Different connectivity topologies, such as scale-free and random networks, are also investigated.

Keywords

Parrondo’s paradox Population dynamics Ecology Game theory Complexity Cooperative Parrondo 

Notes

Funding

Kang Hao Cheong acknowledges the support of SUTD Start-up Research Grant (SRG).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

11071_2019_4788_MOESM1_ESM.pdf (127 kb)
Supplementary material 1 (pdf 127 KB)

References

  1. 1.
    Landa, D., Meirowitz, A.: Game theory, information, and deliberative democracy. Am. J. Polit. Sci. 53, 427–444 (2009)CrossRefGoogle Scholar
  2. 2.
    Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)CrossRefGoogle Scholar
  3. 3.
    Han, Z., Niyato, D., Saad, W., Başar, T., Hjørungnes, A.: Game Theory in Wireless and Communication Networks: Theory, Models, and Applications. Cambridge University Press, Cambridge (2012)zbMATHGoogle Scholar
  4. 4.
    Li, X., Gao, L., Li, W.: Application of game theory based hybrid algorithm for multi-objective integrated process planning and scheduling. Expert Syst. Appl. 39, 288–297 (2012)CrossRefGoogle Scholar
  5. 5.
    Smith, J.M.: The theory of games and the evolution of animal conflicts. J. Theor. Biol. 47, 209–221 (1974)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Samuelson, L.: Evolution and game theory. J. Econ. Perspect. 16, 47–66 (2002)CrossRefGoogle Scholar
  7. 7.
    Harmer, G.P., Abbott, D.: Losing strategies can win by Parrondo’s paradox. Nature 402, 864 (1999)CrossRefGoogle Scholar
  8. 8.
    Harmer, G.P., Abbott, D.: Parrondo’s paradox. Stat. Sci. 14, 206–213 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Parrondo, J.M.R., Harmer, G.P., Abbott, D.: New paradoxical games based on Brownian ratchets. Phys. Rev. Lett. 85, 5226–5229 (2000)CrossRefGoogle Scholar
  10. 10.
    Toral, R.: Cooperative Parrondo’s games. Fluct. Noise Lett. 01, L7–L12 (2001)MathSciNetCrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Harmer, G.P., Abbott, D.: A review of Parrondo’s paradox. Fluct. Noise Lett. 02, R71–R107 (2002)CrossRefGoogle Scholar
  13. 13.
    Abbott, D.: Asymmetry and disorder: a decade of Parrondo’s paradox. Fluct. Noise Lett. 09, 129–156 (2010)CrossRefGoogle Scholar
  14. 14.
    Ajdari, A., Prost, J.: Drift induced by a periodic potential of low symmetry: pulsed dielectrophoresis. C. R. Acad. Sci. Paris Série II 315, 1635–1639 (1993)Google Scholar
  15. 15.
    Rousselet, J., Salome, L., Ajdari, A., Prostt, J.: Directional motion of Brownian particles induced by a periodic asymmetric potential. Nature 370, 446 (1994)CrossRefGoogle Scholar
  16. 16.
    Cao, F.J., Dinis, L., Parrondo, J.M.R.: Feedback control in a collective flashing ratchet. Phys. Rev. Lett. 93, 040603 (2004)CrossRefGoogle Scholar
  17. 17.
    Lee, Y., Allison, A., Abbott, D., Stanley, H.E.: Minimal Brownian ratchet: an exactly solvable model. Phys. Rev. Lett. 91, 220601 (2003)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Danca, M.-F., Fečkan, M., Romera, M.: Generalized form of Parrondo’s paradoxical game with applications to chaos control. Int. J. Bifurcat. Chaos 24, 1450008 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Danca, M.-F., Tang, W.K., Wang, Q., Chen, G.: Suppressing chaos in fractional-order systems by periodic perturbations on system variables. Eur. Phys. J. B 86, 79 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Chau, N.P.: Controlling chaos by periodic proportional pulses. Phys. Lett. A 234, 193–197 (1997)CrossRefGoogle Scholar
  21. 21.
    Allison, A., Abbott, D.: Control systems with stochastic feedback. Chaos 11, 715–724 (2001)CrossRefzbMATHGoogle Scholar
  22. 22.
    Rosato, A., Strandburg, K.J., Prinz, F., Swendsen, R.H.: Why the Brazil nuts are on top: size segregation of particulate matter by shaking. Phys. Rev. Lett. 58, 1038–1040 (1987)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Pinsky, R., Scheutzow, M.: Some remarks and examples concerning the transient and recurrence of random diffusions. Ann. Inst. Henri Poincaré B 28, 519 (1992)zbMATHGoogle Scholar
  24. 24.
    Harmer, G.P., Abbott, D., Taylor, P.G., Pearce, C.E.M., Parrondo, J.M.R.: Information entropy and Parrondo’s discrete-time ratchet. AIP Conf. Proc. 502, 544–549 (2000)CrossRefzbMATHGoogle Scholar
  25. 25.
    Cheong, K.H., Saakian, D.B., Zadourian, R.: Allison mixture and the two-envelope problem. Phys. Rev. E 96, 062303 (2017)CrossRefGoogle Scholar
  26. 26.
    Meyer, D.A., Blumer, H.: Parrondo games as lattice gas automata. J. Stat. Phys. 107, 225–239 (2002)CrossRefzbMATHGoogle Scholar
  27. 27.
    Flitney, A.P., Abbott, D.: Quantum models of Parrondo’s games. Physica A 324, 152–156 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Flitney, A.P., Abbott, D.: An introduction to quantum game theory. Fluct. Noise Lett. 02, R175–R187 (2002)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Lee, C.F., Johnson, N.F., Rodriguez, F., Quiroga, L.: Quantum coherence, correlated noise and Parrondo games. Fluct. Noise Lett. 02, L293–L298 (2002)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Lee, C.F., Johnson, N.F.: Exploiting randomness in quantum information processing. Phys. Lett. A 301, 343–349 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Banerjee, S., Chandrashekar, C.M., Pati, A.K.: Enhancement of geometric phase by frustration of decoherence: a Parrondo-like effect. Phys. Rev. A 87, 042119 (2013)CrossRefGoogle Scholar
  32. 32.
    de Franciscis, S., d’Onofrio, A.: Spatiotemporal bounded noises and transitions induced by them in solutions of the real Ginzburg–Landau model. Phys. Rev. E 86, 021118 (2012)CrossRefGoogle Scholar
  33. 33.
    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)CrossRefGoogle Scholar
  34. 34.
    Reed, F.A.: Two-locus epistasis with sexually antagonistic selection: a genetic Parrondo’s paradox. Genetics 176, 1923–1929 (2007)CrossRefGoogle Scholar
  35. 35.
    Cheong, K.H., Koh, J.M., Jones, M.C.: Entangled mortality: a biological Parrondo’s paradox. Science E-Letter, 29 August 2018. http://science.sciencemag.org/content/360/6393/1075/tabe-letters
  36. 36.
    Wolf, D.M., Vazirani, V.V., Arkin, A.P.: Diversity in times of adversity: probabilistic strategies in microbial survival games. J. Theor. Biol. 234, 227–253 (2005)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Libby, E., Conlin, P.L., Kerr, B., Ratcliff, W.C.: Stabilizing multicellularity through ratcheting. Philos. Trans. R. Soc. B Lond. Biol. Sci. 371, 20150444 (2016)CrossRefGoogle Scholar
  38. 38.
    Cheong, K.H., Koh, J.M., Jones, M.C.: Multicellular survival as a consequence of Parrondo’s paradox. Proc. Natl. Acad. Sci. 115, E5258–5259 (2018)CrossRefGoogle Scholar
  39. 39.
    Williams, P.D., Hastings, A.: Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology. Proc. R. Soc. Lond. B Biol. Sci. 278, 1281–1290 (2011)CrossRefGoogle Scholar
  40. 40.
    Kussell, E., Leibler, S.: Phenotypic diversity, population growth, and information in fluctuating environments. Science 309, 2075–2078 (2005)CrossRefGoogle Scholar
  41. 41.
    Acar, M., van Oudenaarden, J.T.M.A.: Stochastic switching as a survival strategy in fluctuating environments. Nat. Genet. 40, 471 (2008)CrossRefGoogle Scholar
  42. 42.
    Jansen, V.A.A., Yoshimura, J.: Populations can persist in an environment consisting of sink habitats only. Proc. Natl. Acad. Sci. 95, 3696–3698 (1998)CrossRefGoogle Scholar
  43. 43.
    Tan, Z.X., Cheong, K.H.: Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction. eLife 6, e21673 (2017)CrossRefGoogle Scholar
  44. 44.
    Koh, J.M., Xie, N., Cheong, K.H.: Nomadic-colonial switching with stochastic noise: subsidence-recovery cycles and long-term growth. Nonlinear Dyn. 94, 1467–1477 (2018)CrossRefGoogle Scholar
  45. 45.
    Sagués, F., Sancho, J.M., García-Ojalvo, J.: Spatiotemporal order out of noise. Rev. Mod. Phys. 79, 829–882 (2007)CrossRefGoogle Scholar
  46. 46.
    Buceta, J., Lindenberg, K., Parrondo, J.M.R.: Stationary and oscillatory spatial patterns induced by global periodic switching. Phys. Rev. Lett. 88, 024103 (2002)CrossRefGoogle Scholar
  47. 47.
    Lucas, C.H., Graham, W.M., Widmer, C.: Jellyfish life histories: role of polyps in forming and maintaining scyphomedusa populations. Adv. Mar. Biol. 63, 133–196 (2012)CrossRefGoogle Scholar
  48. 48.
    Baldauf, S.L., Doolittle, W.F.: Origin and evolution of the slime molds (mycetozoa). Proc. Natl. Acad. Sci. 94, 12007–12012 (1997)CrossRefGoogle Scholar
  49. 49.
    Bastidas, R.J., Heitman, J.: Trimorphic stepping stones pave the way to fungal virulence. Proc. Natl. Acad. Sci. 106, 351–352 (2009)CrossRefGoogle Scholar
  50. 50.
    Perc, M.: The Matthew effect in empirical data. J. R. Soc. Interface 11, 20140378 (2014)CrossRefGoogle Scholar
  51. 51.
    Courchamp, F., Clutton-Brock, T., Grenfell, B.: Inverse density dependence and the Allee effect. Trends. Ecol. Evol. 14, 405–410 (1999)CrossRefGoogle Scholar
  52. 52.
    Mihailovic, Z., Rajkovic, M.: Synchronous cooperative Parrondo’s games. Fluct. Noise Lett. 03, 389 (2003)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Erdős, P., Rényi, A.: On random graphs i. Publ. Math. Debr. 6, 290–297 (1959)zbMATHGoogle Scholar
  54. 54.
    Gómez-Gardeñes, J., Moreno, Y.: From scale-free to Erdos-Rényi networks. Phys. Rev. E 73, 056124 (2006)CrossRefGoogle Scholar
  55. 55.
    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)CrossRefGoogle Scholar
  56. 56.
    Duan, F., Chapeau-Blondeau, F., Abbott, D.: Stochastic resonance in a parallel array of nonlinear dynamical elements. Phys. Lett. A 372, 2159–2166 (2008)CrossRefzbMATHGoogle Scholar
  57. 57.
    Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70, 223–287 (1998)CrossRefGoogle Scholar
  58. 58.
    Goychuk, I., Hänggi, P.: Non-Markovian stochastic resonance. Phys. Rev. Lett. 91, 070601 (2003)CrossRefGoogle Scholar
  59. 59.
    Dykman, M.I., McClintock, P.V.E.: What can stochastic resonance do? Nature 391, 344 (1998)CrossRefGoogle Scholar
  60. 60.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  61. 61.
    Barabási, A.-L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A 272, 173–187 (1999)CrossRefGoogle Scholar
  62. 62.
    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001)CrossRefGoogle Scholar
  63. 63.
    Kasthurirathna, D., Piraveenan, M.: Emergence of scale-free characteristics in socio-ecological systems with bounded rationality. Sci. Rep. 5, 10448 (2015)CrossRefGoogle Scholar
  64. 64.
    Lieberman, E., Hauert, C., Nowak, M.A.: Evolutionary dynamics on graphs. Nature 433, 312 (2005)CrossRefGoogle Scholar
  65. 65.
    Amaral, L.A.N., Scala, A., Barthélémy, M., Stanley, H.E.: Classes of small-world networks. Proc. Natl. Acad. Sci. 97, 11149–11152 (2000)CrossRefGoogle Scholar
  66. 66.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440 (1998)CrossRefzbMATHGoogle Scholar
  67. 67.
    Kasthurirathna, D., Piraveenan, M., Harré, M.: Influence of topology in the evolution of coordination in complex networks under information diffusion constraints. Eur. Phys. J. B 87, 3 (2014)MathSciNetCrossRefGoogle Scholar
  68. 68.
    Pan, R.K., Sinha, S.: Modular networks with hierarchical organization: the dynamical implications of complex structure. Pramana 71, 331 (2009)CrossRefGoogle Scholar
  69. 69.
    Foley, J.A., et al.: Solutions for a cultivated planet. Nature 478, 337 (2011)CrossRefGoogle Scholar
  70. 70.
    Lineweaver, C.H., Fenner, Y., Gibson, B.K.: The galactic habitable zone and the age distribution of complex life in the milky way. Science 303, 59–62 (2004)CrossRefGoogle Scholar
  71. 71.
    Triandis, H.: Collectivism v. Individualism: A Reconceptualisation of a Basic Concept in Cross-Cultural Social Psychology, pp. 60–95. Palgrave Macmillan, London (1988)Google Scholar
  72. 72.
    Hui, C.: Measurement of individualism-collectivism. J. Res. Personal. 22, 17–36 (1988)CrossRefGoogle Scholar
  73. 73.
    Singh, R.K., Sinha, S.: Optimal interdependence enhances the dynamical robustness of complex systems. Phys. Rev. E 96, 020301 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Science and Math ClusterSingapore University of Technology and DesignSingaporeSingapore
  2. 2.Engineering ClusterSingapore Institute of TechnologySingaporeSingapore

Personalised recommendations