帕隆多悖论

帕隆多悖论（Parrondo's paradox），是博弈论中的悖论，指多个失败策略的组合反成为获胜策略。 1996年，帕隆多发现此悖论。

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，设想一台能从的随机热运动中提取能量的机器。在仔细分析时，有关布朗棘轮的悖论就消失了。 在帕隆多以前，生物学便探索了许多由失败策略组成的致胜策略。

参考

延伸阅读

• 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.

参见

• 巴西果效应
• 布朗棘轮
• 博弈论
• 悖论列表
• 统计力学

外部链接

• 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）.