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Reversals of chance in paradoxical games

Author

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  • Amengual, P.
  • Meurs, P.
  • Cleuren, B.
  • Toral, R.

Abstract

We present two collective games with new paradoxical features when they are combined. Besides reproducing the so-called Parrondo effect, where a winning game is obtained from the alternation of two fair games, there also exists a current inversion when varying the mixing probability between the games. We show that this is a new effect insofar one of the games is an unbiased random walk without internal structure. We present a detailed study by means of a discrete-time Markov chain analysis, obtaining analytical expressions for the stationary probabilities for a finite number of players. We also provide qualitative insight into this current inversion effect.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:371:y:2006:i:2:p:641-648
    DOI: 10.1016/j.physa.2006.03.038
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Mendoza, Steve A. & Peacock-López, Enrique, 2018. "Switching induced oscillations in discrete one-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 35-44.
    2. Levinsohn, Erik A. & Mendoza, Steve A. & Peacock-López, Enrique, 2012. "Switching induced complex dynamics in an extended logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 426-432.

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