The coupling effect of the process sequence and the parity of the initial capital on Parrondo’s games

Wang, Lu; Zhu, Yong-fei; Ye, Ye; Meng, Rui; Xie, Nenggang

doi:10.1016/j.physa.2012.06.008

Cited by 2 publications

(2 citation statements)

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“…Moreover, starting at different initial states, we deduce the probabilities of absorption at the two absorbing barriers. The current studies on Parrondo's games have shown rich nonlinear phenomena: (i) two losing games can produce a winning game; (ii) fractal patterns [25]; (iii) the orderly process can produce an uncertain value, whereas the disorderly process can produce a certain value [26][27][28]; (iv) chaos 1 + chaos 2 + · · · + chaos N = order [29]. The results of this study show random walks in the presence of two absorbing barriers in Parrondo's games.…”

Section: Resultsmentioning

confidence: 99%

“…Allison's [25] findings have shown that Parrondo's games exhibit fractal patterns in their state space. Xie [26][27][28] studied the coupling effect of the process sequence and the parity of the initial capital on Parrondo's games. The results demonstrated that the initial value and the processes had the coupling effects on the final states, that is, "deterministic mixing leads to win or lose depending on the parity of the initial capital and random mixing leads to a deterministic result".…”

Section: Introductionmentioning

confidence: 99%

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Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

et al. 2014

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Communicated by Stefania ResidoriFor a multi-agent spatial Parrondo's model that it is composed of games A and B, we use the discrete time Markov chains to derive the probability transition matrix. Then, we respectively deduce the stationary distribution for games A and B played individually and the randomized combination of game A + B. We notice that under a specific set of parameters, two absorbing states instead of a fixed stationary distribution exist in game B. However, the randomized game A + B can jump out of the absorbing states of game B and has a fixed stationary distribution because of the "agitating" role of game A. Moreover, starting at different initial states, we deduce the probabilities of absorption at the two absorbing barriers.

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