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Parrondo's games as a discrete ratchet

Author

Listed:
  • Toral, R.
  • Amengual, Pau
  • Mangioni, Sergio

Abstract

We write the master equation describing the Parrondo's games as a consistent discretization of the Fokker–Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the relation between ratchets and Parrondo's games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials correspond to fair games and winning games produce a tilted potential.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:327:y:2003:i:1:p:105-110
    DOI: 10.1016/S0378-4371(03)00459-X
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    Cited by:

    1. Song, Mi Jung & Lee, Jiyeon, 2021. "An approximation by Parrondo games of the Brownian ratchet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    2. Amengual, P. & Meurs, P. & Cleuren, B. & Toral, R., 2006. "Reversals of chance in paradoxical games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 641-648.
    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.
    4. Breuer, Sandro & Mielke, Andreas, 2023. "Multi player Parrondo games with rigid coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).

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