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Theoretical analysis and numerical simulation of Parrondo’s paradox game in space

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  • Xie, Neng-gang
  • Chen, Yun
  • Ye, Ye
  • Xu, Gang
  • Wang, Lin-gang
  • Wang, Chao

Abstract

A multi-agent spatial Parrondo game model is designed according to the cooperative Parrondo’s paradox proposed by Toral. The model is composed of game A and game B. Game A is a zero-sum game between individuals, reflecting competitive interaction between an individual and its neighbors. The winning or losing probability of one individual in game B depends on its neighbors’ winning or losing states, reflecting the dependence that individuals has on microhabitat and the overall constraints that the microhabitat has on individuals. By using the analytical approach based on discrete-time Markov chain, we analyze game A, game B and the random combination of game A+B, and obtain corresponding stationary distribution probability and mathematical expectations. We have established conditions of the weak and strong forms of the Parrondo effect, and compared the computer simulation results with the analytical results so as to verify their validity. The analytical results reflect that competition results in the ratchet effect of game B, which generates Parrondo’s Paradox that the combination of the losing games can produce a winning result.

Suggested Citation

  • Xie, Neng-gang & Chen, Yun & Ye, Ye & Xu, Gang & Wang, Lin-gang & Wang, Chao, 2011. "Theoretical analysis and numerical simulation of Parrondo’s paradox game in space," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 401-414.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:6:p:401-414
    DOI: 10.1016/j.chaos.2011.01.014
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    References listed on IDEAS

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    1. 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.
    2. Mihailović, Zoran & Rajković, Milan, 2006. "Cooperative Parrondo's games on a two-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 244-251.
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    1. Li, Yin-feng & Ye, Shun-qiang & Zheng, Kai-xuan & Xie, Neng-gang & Ye, Ye & Wang, Lu, 2014. "A new theoretical analysis approach for a multi-agent spatial Parrondo’s game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 369-379.
    2. Ye, Ye & Xie, Neng-gang & Wang, Lu & Cen, Yu-wan, 2013. "The multi-agent Parrondo’s model based on the network evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5414-5421.

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