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Occurrence of complementary processes in Parrondo’s paradox

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  • Soo, Wayne Wah Ming
  • Cheong, Kang Hao

Abstract

Parrondo’s paradox involves two losing processes producing a winning outcome. We analyze the paradox with an original and novel method in which we start with one process and seek to construct a complementary process to achieve the paradox. We then derive a general condition for the classical Parrondo game to have a complementary process. Numerical simulation predicts that approximately two-thirds of such losing games satisfy the required condition. This suggests the common occurrence of the paradox, indicative of many potentially undiscovered applications in real-life scenarios involving stochastic processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:412:y:2014:i:c:p:180-185
    DOI: 10.1016/j.physa.2014.06.010
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
    4. Toral, R. & Amengual, Pau & Mangioni, Sergio, 2003. "Parrondo's games as a discrete ratchet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(1), pages 105-110.
    5. Dinís, Luis & Parrondo, Juan M.R., 2004. "Inefficiency of voting in Parrondo games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 701-711.
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    Cited by:

    1. 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).

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