Parrondo Games with Spatial Dependence and a Related Spin System, II

Title
Parrondo Games with Spatial Dependence and a Related Spin System, II
Author(s)
이지연S. N. Ethier[S. N. Ethier]
Keywords
PARADOX; REDISTRIBUTION; WEALTH
Issue Date
201312
Publisher
POLYMAT
Citation
MARKOV PROCESSES AND RELATED FIELDS, v.19, no.4, pp.667 - 692
Abstract
Let game B be Toral's cooperative Parrondo game with (one-dimensional) spatial dependence, parameterized by N >= 3 and p(0), p(1), p(2), p(3) is an element of [0,1], and let game A be the special case p(0) = p(1) = p(2) = p(3) = 1/2. Let mu(N)(B) (resp., mu(N)((1/2,1/2))) denote the mean profit per turn to the ensemble of N players always playing game B (resp., always playing the randomly mixed game (1/2) (A+B)). In previous work we showed that, under certain conditions, both sequences converge and the limits can be expressed in terms of a parameterized spin system on the one-dimensional integer lattice. Of course one can get similar results for mu(N)((gamma,1-gamma)) corresponding to gamma A + (1 - gamma)B for 0 < gamma < 1. 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, under certain conditions, mu(N)([r,s]), the mean profit per turn to the ensemble of N players repeatedly playing the pattern A(r)B(s), converges to the same limit that mu(N)((gamma,1-gamma)) converges to, where gamma := r/(r + s).
URI
http://hdl.handle.net/YU.REPOSITORY/28043
ISSN
1024-2953
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이과대학 > 통계학과 > Articles
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