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A redistribution model of the history-dependent Parrondo game

과거의존 파론도 게임의 재분배 모형

  • Received : 2014.11.20
  • Accepted : 2014.12.19
  • Published : 2015.01.31

Abstract

Parrondo paradox is the counter-intuitive phenomenon where two losing games can be combined to win or two winning games can be combined to lose. In this paper, we consider an ensemble of players, one of whom is chosen randomly to play game A' or game B. In game A', the randomly chosen player transfers one unit of his capital to another randomly selected player. In game B, the player plays the history-dependent Parrondo game in which the winning probability of the present trial depends on the results of the last two trials in the past. We show that Parrondo paradox exists in this redistribution model of the history-dependent Parrondo game.

Keywords

Expected profits;history-dependent Parrondo games;Markov chains;Parrondo paradox;redistribution models;stationary distriburions

References

  1. Cho, D. and Lee, J. (2012a). Parrondo paradox and stock investment. Korean Journal of Applied Statistics, 25, 543-552. https://doi.org/10.5351/KJAS.2012.25.4.543
  2. Cho, D. and Lee, J. (2012b). Spatially dependent Parrondo games and stock investments. Journal of the Korean Data & Information Science Society, 23, 867-880. https://doi.org/10.7465/jkdi.2012.23.5.867
  3. Ethier, S. N. (2007) Markov chains and Parrondo's paradox. In Optimal Play: Mathematical Studies of Games and Gambling, edited by S. N. Ethier and W. R. Eadington, Institute for the Study of Gambling and Commercial Gaming, University of Nevada, Reno, 493-506.
  4. Ethier, S. N. and Lee, J. (2009). Limit theorems for Parrondo's paradox. Electronic Journal of Probability, 14, 1827-1862. https://doi.org/10.1214/EJP.v14-684
  5. Ethier, S. N. and Lee, J. (2012). Parrondo's paradox via redistribution of wealth. Electronic Journal of Probability, 17, no. 20, 1-21.
  6. Harmer, G. P., Abbott, D., Taylor, P. G., and Parrondo, J. M. R. (2001). Brownian ratchets and Parrondo's games. Chaos, 11, 705-714. https://doi.org/10.1063/1.1395623
  7. Harmer, G. P. and Abbott, D. (2002). A review of Parrondo's paradox. Fluctuation and Noise Letters, 2, R71-R107. https://doi.org/10.1142/S0219477502000701
  8. Lee, J. (2009). Optimal strategies for collective Parrondo games. Journal of the Korean Data & Information Science Society, 20, 973-982.
  9. Lee, J. (2011). Paradox in collective history-dependent Parrondo games. Journal of the Korean Data & Information Science Society, 22, 631-641.
  10. Parrondo, J. M. R. (1996). How to cheat a bad mathematician? In the Workshop of the EEC HC&M Network on Complexity and Chaos, ISI, Torino, Italy. Unpublished.
  11. Parrondo, J. M. R., Harmer, G. P. and Abbott, D. (2000). New paradoxical games based on Brownian ratchets. Physical Review Letters, 85, 5226-5229. https://doi.org/10.1103/PhysRevLett.85.5226
  12. Toral, R (2002). Capital redistribution brings wealth by Parrondo's paradox. Fluctuation and Noise Letters, 2, L305-L311. https://doi.org/10.1142/S0219477502000907

Cited by

  1. Stock investment with a redistribution model of the history-dependent Parrondo game vol.26, pp.4, 2015, https://doi.org/10.7465/jkdi.2015.26.4.781
  2. A redistribution model for spatially dependent Parrondo games vol.27, pp.1, 2016, https://doi.org/10.7465/jkdi.2016.27.1.121

Acknowledgement

Supported by : 한국연구재단