Abstract
A minimalistic multi-agent Parrondo’s game structure with branching dependent on local capital spread was previously introduced, indicating that stochastically mixing two losing games can produce winning outcomes with bounded capital variance among players. Using a similar game structure, we unveil further intriguing behavior that a bias toward selfish exploitative behavior, involving redistribution of capital from the poor to the rich, leads to counterintuitive superior capital gains than cooperative behaviors. Inter-agent interactions of exploitative nature not only maximizes capital growth in winning scenarios, but also expands the parameter space over which the Parrondo effect may manifest. These novel findings suggest a link between growth maximization and inequality that could be relevant to socioeconomic, ecological, and population dynamics modeling. We also present a theoretical framework for enhanced accuracy in the prediction of ensemble capital statistics.
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West, S.A., Gardner, A., Shuker, D.M., Reynolds, T., Burton-Chellow, M., Sykes, E.M., Guinnee, M.A., Griffin, A.S.: Cooperation and the scale of competition in humans. Curr. Biol. 16, 1103 (2006)
Wilson, D.S., Near, D.C., Miller, R.R.: Individual differences in machiavellianism as a mix of cooperative and exploitative strategies. Evol. Hum. Behav. 19, 203 (1998)
Simon, H.A.: Theories of decision-making in economics and behavioral science. Am. Econ. Rev. 49, 253 (1959)
Smith, J.M.: Game theory and the evolution of behaviour. Behav. Brain Sci. 7, 95 (1984)
Harmer, G.P., Abbott, D.: Losing strategies can win by Parrondo’s paradox. Nature 402, 864 (1999a)
Harmer, G.P., Abbott, D.: Parrondo’s paradox. Stat. Sci. 14, 206 (1999b)
Parrondo, J.M.R., Harmer, G.P., Abbott, D.: New paradoxical games based on Brownian ratchets. Phys. Rev. Lett. 85, 5226 (2000)
Ajdari, A., Prost, J.: Drift induced by a periodic potential of low symmetry: pulsed dielectrophoresis. C. R. Acad. Sci. Paris Sér. 315, 1635 (1993)
Rousselet, J., Salome, L., Ajdari, A., Prostt, J.: Directional motion of brownian particles induced by a periodic asymmetric potential. Nature 370, 446 (1994)
Cao, F.J., Dinis, L., Parrondo, J.M.R.: Feedback control in a collective flashing ratchet. Phys. Rev. Lett. 93, 040603 (2004)
Toral, R.: Cooperative Parrondo’s games. Fluct. Noise Lett. 01, L7 (2001)
Toral, R.: Capital redistribution brings wealth by Parrondo’s paradox. Fluct. Noise Lett. 02, L305 (2002)
Danca, M.-F., Fečkan, M., Romera, M.: Generalized form of Parrondo’s paradoxical game with applications to chaos control. Int. J. Bifurc. Chaos 24, 1450008 (2014)
Chau, N.P.: Controlling chaos by periodic proportional pulses. Phys. Lett. A 234, 193 (1997)
Allison, A., Abbott, D.: Control systems with stochastic feedback. Chaos 11, 715 (2001)
Danca, M.-F., Lai, D.: Parrodo’s game model to find numerically stable attractors of a tumour growth model. Int J Bifurc Chaos 22, 1250258 (2012)
Danca, M.-F., Tang, W.K.S.: Parrondo’s paradox for chaos control and anticontrol of fractional-order systems. Chin. Phys. B 25, 010505 (2016)
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 (1987)
Pinsky, R., Scheutzow, M.: Some remarks and examples concerning the transient and recurrence of random diffusions. Ann. Inst. Henri Poincaré B 28, 519 (1992)
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 (2000)
Pearce, C.E.M.: Entropy, Markov information sources and Parrondo games. AIP Conf. Proc. 511, 207 (2000)
Cheong, K.H., Saakian, D.B., Zadourian, R.: Allison mixture and the two-envelope problem. Phys. Rev. E 96, 062303 (2017)
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 (2005)
Libby, E., Conlin, P.L., Kerr, B., Ratcliff, W.C.: Stabilizing multicellularity through ratcheting. Philos. Trans. R. Soc. B 371 (2016). https://doi.org/10.1098/rstb.2015.0444
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). https://doi.org/10.1038/srep34889
Tan, Z.X., Cheong, K.H.: Nomadic-colonial life strategies enable paradoxical survival and growth despite habitat destruction. eLife 6, e21673 (2017). https://doi.org/10.7554/eLife.21673
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 (2018)
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). https://www.pnas.org/content/115/23/E5258
Cheong, K.H., Koh, J.M., Jones, M.C.: Paradoxical survival: Examining the parrondo effect across biology. BioEssays 41, 1900027 (2019). https://doi.org/10.1002/bies.201900027
Meyer, D.A., Blumer, H.: Parrondo games as lattice gas automata. J. Stat. Phys. 107, 225 (2002)
Flitney, A.P., Abbott, D., Johnson, N.F.: Quantum walks with history dependence. J. Phys. A Math. Gen. 37, 7581 (2004)
Rajendran, J., Benjamin, C.: Implementing Parrondo’s paradox with two-coin quantum walks. Open Sci. (2018). https://doi.org/10.1098/rsos.171599. http://rsos.royalsocietypublishing.org/content/5/2/171599.full.pdf
Rajendran, J., Benjamin, C.: Playing a true Parrondo’s game with a three-state coin on a quantum walk. EPL (Europhys. Lett.) 122, 40004 (2018)
Flitney, A.P., Abbott, D.: Quantum models of Parrondo’s games. Phys. A 324, 152 (2003)
Flitney, A.P., Abbott, D.: An introduction to quantum game theory. Fluct. Noise Lett. 02, R175 (2002)
Lee, C.F., Johnson, N.F., Rodriguez, F., Quiroga, L.: Quantum coherence, correlated noise and Parrondo Games. Fluct. Noise Lett. 02, L293 (2002)
Lee, C.F., Johnson, N.F.: Exploiting randomness in quantum information processing. Phys. Lett. A 301, 343 (2002)
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)
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)
Pejic, M.: Quantum Bayesian networks with application to games displaying Parrondo’s paradox. (2015), ArXiv e-prints arXiv:1503.08868
Di Crescenzo, A.: A Parrondo paradox in reliability theory. Math. Sci. 32, 17 (2007)
Zhang, Y., Luo, G.: A special type of codimension two bifurcation and unusual dynamics in a phase-modulated system with switched strategy. Nonlinear Dyn. 67, 2727–2734 (2012)
Zhang, Y.: Switching-induced Wada basin boundaries in the Hénon map. Nonlinear Dyn. 73, 2221–2229 (2013)
Danca, M.-F.: Convergence of a parameter switching algorithm for a class of nonlinear continuous systems and a generalization of Parrondo’s paradox. Commun. Nonlinear Sci. Numer. Simul. 18, 500–510 (2013)
Koh, J.M., Cheong, K.H.: Automated electron-optical system optimization through switching Levenberg–Marquardt algorithms. J. Electron Spectrosc. Relat. Phenom. 227, 31 (2018)
Koh, J.M., Cheong, K.H.: New doubly-anomalous Parrondo’s games suggest emergent sustainability and inequality. Nonlinear Dyn. 96, 257 (2019)
Triandis, H.C.: Individualism–Collectivism and Personality. J. Personal. 69, 907 (2001)
Hui, C.H.: Measurement of individualism–collectivism. J. Res. Personal. 22, 17 (1988)
Mihailovic, Z., Rajkovic, M.: Synchronous cooperative Parrondo’s games. Fluct. Noise Lett. 03, 389 (2003)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509 (1999)
Barabási, A.-L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Phys. A 272, 173 (1999)
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)
Kasthurirathna, D., Piraveenan, M.: Emergence of scale-free characteristics in socio-ecological systems with bounded rationality. Sci. Rep. 5, 10448 (2015)
Gao, J., Barzel, B., Barabasi, A.L.: Universal resilience patterns in complex networks. Nature 530, 307 (2016)
Amaral, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of small-world networks. Proc. Natl. Acad. Sci. 97, 11149 (2000)
Erdős, P., Rényi, A.: On random graphs I. Publ. Math. Debr. 6, 290 (1959)
Gómez-Gardeñes, J., Moreno, Y.: From scale-free to Erdos–Rényi networks. Phys. Rev. E 73, 056124 (2006)
Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393, 440 (1998)
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). https://doi.org/10.1038/srep37028
Miller, S., Diamond, J.: A new world of differences. Nature 441, 411 (2006)
Sargent, M.: Why inequality is fatal. Nature 458, 1109 (2009)
Bechhoefer, J.: Feedback for physicists: a tutorial essay on control. Rev. Mod. Phys. 77, 783 (2005)
Saavedra, S., Reed-Tsochas, F., Uzzi, B.: A simple model of bipartite cooperation for ecological and organizational networks. Nature 457, 463 (2008)
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This project was supported by the SUTD Start-up Research Grant (SRG).
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Koh, J.M., Cheong, K.H. Emergent preeminence of selfishness: an anomalous Parrondo perspective. Nonlinear Dyn 98, 943–951 (2019). https://doi.org/10.1007/s11071-019-05237-6
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DOI: https://doi.org/10.1007/s11071-019-05237-6