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Parrondo’s paradox and complementary Parrondo processes

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  • Soo, Wayne Wah Ming
  • Cheong, Kang Hao

Abstract

Parrondo’s Paradox has gained a fair amount of attention due to it being counter-intuitive. Given two stochastic processes, both of which are losing in nature, it is possible to have an overall net increase in capital by periodically or randomly alternating between the two processes. In this paper, we analyze the paradox with a different approach, in which we start with one process and seek to derive its complementary process. We will also state the conditions required for this to occur. Possible applications of our results include the development of future models based on the paradox.

Suggested Citation

  • Soo, Wayne Wah Ming & Cheong, Kang Hao, 2013. "Parrondo’s paradox and complementary Parrondo processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 17-26.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:1:p:17-26
    DOI: 10.1016/j.physa.2012.08.006
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    References listed on IDEAS

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    1. N. Masuda & N. Konno, 2004. "Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 40(3), pages 313-319, August.
    2. Flitney, A.P. & Abbott, D., 2003. "Quantum models of Parrondo's games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 152-156.
    3. Flitney, A.P. & Ng, J. & Abbott, D., 2002. "Quantum Parrondo's games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 35-42.
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    Cited by:

    1. Cheong, Kang Hao & Soo, Wayne Wah Ming, 2013. "Construction of novel stochastic matrices for analysis of Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4727-4738.
    2. Jia, Shuyi & Lai, Joel Weijia & Koh, Jin Ming & Xie, Neng Gang & Cheong, Kang Hao, 2020. "Parrondo effect: Exploring the nature-inspired framework on periodic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    3. Soo, Wayne Wah Ming & Cheong, Kang Hao, 2014. "Occurrence of complementary processes in Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 180-185.

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