The paradox of Parrondo's games

被引：58

作者：

Harmer, GP ^{[1
]}

Abbott, D

Taylor, PG

机构：

[1] Univ Adelaide, Ctr Biomed Engn, CBME, Adelaide, SA 5005, Australia

[2] Univ Adelaide, Dept Elect & Elect Engn, Adelaide, SA 5005, Australia

[3] Univ Adelaide, Dept Appl Math, Adelaide, SA 5005, Australia

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2000年 / 456卷 / 1994期

关键词：

gambling paradox; Brownian ratchet; discrete-time Markov chains;

D O I：

10.1098/rspa.2000.0516

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We introduce Parrondo's paradox that involves games of chance. We consider two fair games, A and B, both of which can be made to lose by changing a biasing parameter. An apparently paradoxical situation arises when the two games are played in any alternating order. A winning expectation is produced, even though both games A and B are losing when we play them individually. We develop an explanation of the phenomenon in terms of a Brownian ratchet model, and also develop a mathematical analysis using discrete-time Markov chains. From the analysis we investigate the range of parameter values for which Parrondo's paradox exists.

引用

页码：247 / 259

页数：13

共 17 条

[1]

ABBOTT D, 2000, IN PRESS P 2 INT C U

[2] FLUCTUATION DRIVEN RATCHETS - MOLECULAR MOTORS [J].

ASTUMIAN, RD ;

BIER, M .

PHYSICAL REVIEW LETTERS, 1994, 72 (11) :1766-1769

[3] Thermodynamics and kinetics of a Brownian motor [J].

Astumian, RD .

SCIENCE, 1997, 276 (5314) :917-922

[4] Brownian ratchets in physics and biology [J].

Bier, M .

CONTEMPORARY PHYSICS, 1997, 38 (06) :371-379

[5]

BIER M, 1997, STOCH DYNAM, V386, P81

[6] RANDOMLY RATTLED RATCHETS [J].

DOERING, CR .

NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA D-CONDENSED MATTER ATOMIC MOLECULAR AND CHEMICAL PHYSICS FLUIDS PLASMAS BIOPHYSICS, 1995, 17 (7-8) :685-697

[7] OPTICAL THERMAL RATCHET [J].

FAUCHEUX, LP ;

BOURDIEU, LS ;

KAPLAN, PD ;

LIBCHABER, AJ .

PHYSICAL REVIEW LETTERS, 1995, 74 (09) :1504-1507

[8]

FEYNMAN RP, 1963, FEYNMAN LECT PHYSICS, V1

[9]

Haenggi P., 1996, Nonlinear physics of complex systems. Current status and future trends, P294

[10]

Harmer GP, 1999, STAT SCI, V14, P206

← 1 2 →