PARRONDO GAMES WITH SPATIAL DEPENDENCE, II

Title
PARRONDO GAMES WITH SPATIAL DEPENDENCE, II
Author(s)
이지연S. N. Ethier[S. N. Ethier]
Keywords
PARADOX; REDISTRIBUTION; WEALTH
Issue Date
201212
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Citation
FLUCTUATION AND NOISE LETTERS, v.11, no.4
Abstract
Let game B be Toral's cooperative Parrondo game with (one-dimensional) spatial dependence, parameterized by N >= 3 and p0, p1, p2, p3 is an element of [0, 1], and let game A be the special case p0 = p1 = p2 = p3 = 1/2. In previous work we investigated mu B and mu(1/2,1/2), the mean profits per turn to the ensemble of N players always playing game B and always playing the randomly mixed game (1/2)(A + B). These means were computable for 3 <= N <= 19, at least, and appeared to converge as N -> infinity, suggesting that the Parrondo region (i.e., the region in which mu B <= 0 and mu((1/2,1/2)) > 0) has nonzero volume in the limit. The convergence was established under certain conditions, and the limits were expressed in terms of a parameterized spin system on the one-dimensional integer lattice. In this paper we replace the random mixture with the nonrandom periodic pattern A(r)B(s), where r and s are positive integers. We show that mu([r,s]), the mean profit per turn to the ensemble of N players repeatedly playing the pattern A(r)B(s), is computable for 3 <= N <= 18 and r + s <= 4, at least, and appears to converge as N -> infinity, albeit more slowly than in the random-mixture case. Again this suggests that the Parrondo region (mu(B) <= 0 and mu([r,s]) > 0) has nonzero volume in the limit. Moreover, we can prove this convergence under certain conditions and identify the limits.
URI
http://hdl.handle.net/YU.REPOSITORY/26854http://dx.doi.org/10.1142/S0219477512500307
ISSN
0219-4775
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이과대학 > 통계학과 > Articles
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