帕隆多悖论

帕隆多悖论（Parrondo's paradox），是博弈论中的悖论，指多個失败策略的组合反成为获胜策略。 1996年，帕隆多（英语：J._M._R._Parrondo）发现此悖论。 帕隆多在对布朗棘轮的分析中设计此悖论。布朗棘轮是物理学家费曼的思想实验，設想一台能从的随机热运动中提取能量的機器。在仔細分析时，有關布朗棘轮的悖论就消失了。 在帕隆多以前，生物学便探索了許多由失败策略组成的致胜策略。 Harmer, G. P.; Abbott, D. Losing strategies can win by Parrondo's paradox. Nature. 1999, 402 (6764): 864. S2CID 41319393. doi:10.1038/47220 .  Shu, Jian-Jun; Wang, Q.-W. Beyond Parrondo's paradox. Scientific Reports. 2014, 4 (4244): 4244. Bibcode:2014NatSR...4E4244S. PMC 5379438 . PMID 24577586. arXiv:1403.5468 . doi:10.1038/srep04244.  Jansen, V. A. A.; Yoshimura, J. Populations can persist in an environment consisting of sink habitats only. Proceedings of the National Academy of Sciences USA. 1998, 95 (7): 3696–3698. Bibcode:1998PNAS...95.3696J. PMC 19898 . PMID 9520428. doi:10.1073/pnas.95.7.3696 . . John Allen Paulos, A Mathematician Plays the Stock Market, Basic Books, 2004, ISBN 0-465-05481-1. Neil F. Johnson, Paul Jefferies, Pak Ming Hui, Financial Market Complexity, Oxford University Press, 2003, ISBN 0-19-852665-2. Ning Zhong and Jiming Liu, Intelligent Agent Technology: Research and Development, World Scientific, 2001, ISBN 981-02-4706-0. Elka Korutcheva and Rodolfo Cuerno, Advances in Condensed Matter and Statistical Physics, Nova Publishers, 2004, ISBN 1-59033-899-5. Maria Carla Galavotti, Roberto Scazzieri, and Patrick Suppes, Reasoning, Rationality, and Probability, Center for the Study of Language and Information, 2008, ISBN 1-57586-557-2. Derek Abbott and Laszlo B. Kish, Unsolved Problems of Noise and Fluctuations, American Institute of Physics, 2000, ISBN 1-56396-826-6. Visarath In, Patrick Longhini, and Antonio Palacios, Applications of Nonlinear Dynamics: Model and Design of Complex Systems, Springer, 2009, ISBN 3-540-85631-5. Marc Moore, Sorana Froda, and Christian Léger, Mathematical Statistics and Applications: Festschrift for Constance van Eeden, IMS, 2003, ISBN 0-940600-57-9. Ehrhard Behrends, Fünf Minuten Mathematik: 100 Beiträge der Mathematik-Kolumne der Zeitung Die Welt, Vieweg+Teubner Verlag, 2006, ISBN 3-8348-0082-1. Lutz Schimansky-Geier, Noise in Complex Systems and Stochastic Dynamics, SPIE, 2003, ISBN 0-8194-4974-1. Susan Shannon, Artificial Intelligence and Computer Science, Nova Science Publishers, 2005, ISBN 1-59454-411-5. Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 2003, ISBN 1-58488-347-2. David Reguera, José M. G. Vilar, and José-Miguel Rubí, Statistical Mechanics of Biocomplexity, Springer, 1999, ISBN 3-540-66245-6. Sergey M. Bezrukov, Unsolved Problems of Noise and Fluctuations, Springer, 2003, ISBN 0-7354-0127-6. Julian Chela-Flores, Tobias C. Owen, and F. Raulin, First Steps in the Origin of Life in the Universe, Springer, 2001, ISBN 1-4020-0077-4. Tönu Puu and Iryna Sushko, Business Cycle Dynamics: Models and Tools, Springer, 2006, ISBN 3-540-32167-5. Andrzej S. Nowak and Krzysztof Szajowski, Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control, Birkhäuser, 2005, ISBN 0-8176-4362-1. Cristel Chandre, Xavier Leoncini, and George M. Zaslavsky, Chaos, Complexity and Transport: Theory and Applications, World Scientific, 2008, ISBN 981-281-879-0. Richard A. Epstein, The Theory of Gambling and Statistical Logic (Second edition), Academic Press, 2009, ISBN 0-12-374940-9. Clifford A. Pickover, The Math Book, （页面存档备份，存于互联网档案馆） Sterling, 2009, ISBN 1-4027-5796-4. 巴西果效应 布朗棘轮 博弈论 悖论列表 统计力学 J. M. R. Parrondo, Parrondo's paradoxical games Nature news article on Parrondo's paradox （页面存档备份，存于互联网档案馆） Parrondo's Paradox - A Simulation （页面存档备份，存于互联网档案馆） Parrondo's Paradox （页面存档备份，存于互联网档案馆） at Futility Closet Parrondo's Paradox at Wolfram （页面存档备份，存于互联网档案馆） Online Parrondo simulator （页面存档备份，存于互联网档案馆） Parrondo's paradox at Maplesoft （页面存档备份，存于互联网档案馆） Optimal adaptive strategies and Parrondo Reed, Floyd A. Two-Locus Epistasis With Sexually Antagonistic Selection: A Genetic Parrondo's Paradox. Genetics (Oxford). 1 July 2007, 176 (3): 1923–1929 [29 April 2023]. PMID 17483431. S2CID 28986153. doi:10.1534/genetics.106.069997. （原始内容存档于2023-04-29）.