Parrondo’s Capital and History-Dependent Games
It has been shown that it is possible to construct two games that when played individually lose, but alternating randomly or deterministically between them can win. This apparent paradox has been dubbed “Parrondo’s paradox.” The original games are capital-dependent, which means that the winning and losing probabilities depend on how much capital the player currently has. Recently, new games have been devised, that are not capital-dependent, but historydependent. We present some analytical results using discrete-time Markovchain theory, which is accompanied by computer simulations of the games.
KeywordsTransition Matrix Physical Review Letter Original Game Markov Chain Theory Brownian Ratchet
Unable to display preview. Download preview PDF.
- Adjari A. and Prost J., Drift induced by a periodic potential of low symmetry: pulsed dielectrophoresis. C. R. Academy of Science Paris, Série II, 315:1635–1639, 1992.Google Scholar
- Harmer G. P., Abbott D., Taylor P. G. and Parrondo J. M. R., Parrondo’s paradoxical games and the discrete Brownian ratchet. In D. Abbott and L. B. Kish, editors, Second International Conference on Unsolved Problems of Noise and Fluctuations, volume 511, pages 189–200, Adelaide, Australia, American Institute of Physics, 2000.Google Scholar
- Harmer G. P., Abbott D., Taylor P. G. and Parrondo J. M. R., Parrondo’s games and Brownian ratchets. Chaos 11(3):705–714.Google Scholar
- Costa A., Fackrell M. and Taylor P. G., Two issues surrounding Parrondo’s paradox. Birkhäuser Annals of Dynamic Games, This volume, 2004.Google Scholar
- Pearce C. E. M., Entropy, Markov information sources and Parrondo games. In D. Abbott and L. B. Kish, editors, Second International Conference on Unsolved Problems of Noise and Fluctuations, volume 511, pages 207–212, Adelaide, Australia, American Institute of Physics, 2000.Google Scholar
- Pyke R., On random walks related to Parrondo’s games. Preprint math. PR/0206150, 2001.Google Scholar