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Quantum game interpretation for a special case of Parrondo’s paradox

Author

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  • Zhu, Yong-fei
  • Xie, Neng-gang
  • Ye, Ye
  • Peng, Fa-rui

Abstract

By using the discrete Markov chain method, Parrondo’s paradox is studied by means of theoretical analysis and computer simulation, built on the case of game AB played in alternation with modulus M=4. We find that such a case does not have a definite stationary probability distribution and that payoffs of the game depend on the parity of the initial capital. Besides, this paper reveals the phenomenon that “processing in order produces non-deterministic results, while a random process produces deterministic results”. The quantum game method is used in a further study. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.

Suggested Citation

  • Zhu, Yong-fei & Xie, Neng-gang & Ye, Ye & Peng, Fa-rui, 2011. "Quantum game interpretation for a special case of Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 579-586.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:4:p:579-586
    DOI: 10.1016/j.physa.2010.10.039
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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. 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.
    3. 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.
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    1. Wang, Lu & Zhu, Yong-fei & Ye, Ye & Meng, Rui & Xie, Neng-gang, 2012. "The coupling effect of the process sequence and the parity of the initial capital on Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5197-5207.
    2. Zhang, Cuihua & Xing, Peng, 2015. "A research on service quality decision-making of Chinese communications industry based on quantum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 9-15.
    3. Wang, Lu & Xie, Neng-gang & Zhu, Yong-fei & Ye, Ye & Meng, Rui, 2011. "Parity effect of the initial capital based on Parrondo’s games and the quantum interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4535-4542.

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