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，4=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**

**脚注**

**延伸阅读**
 John Allen Paulos,  A Mathematician Plays the Stock Market, Basic Books, 2004, 0-465-05481-1.- Neil F. Johnson, Paul Jefferies, Pak Ming Hui,  Financial Market Complexity, Oxford University Press, 2003, 0-19-852665-2.- Ning Zhong and Jiming Liu,  Intelligent Agent Technology: Research and Development, World Scientific, 2001, 981-02-4706-0.- Elka Korutcheva and Rodolfo Cuerno,  Advances in Condensed Matter and Statistical Physics, Nova Publishers, 2004, 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, 1-57586-557-2.- Derek Abbott and Laszlo B. Kish,  Unsolved Problems of Noise and Fluctuations, American Institute of Physics, 2000, 1-56396-826-6.- Visarath In, Patrick Longhini, and Antonio Palacios,  Applications of Nonlinear Dynamics: Model and Design of Complex Systems, Springer, 2009, 3-540-85631-5.- Marc Moore, Sorana Froda, and Christian Léger,  Mathematical Statistics and Applications: Festschrift for Constance van Eeden, IMS, 2003, 0-940600-57-9.- Ehrhard Behrends,  Fünf Minuten Mathematik: 100 Beiträge der Mathematik-Kolumne der Zeitung Die Welt, Vieweg+Teubner Verlag, 2006, 3-8348-0082-1.- Lutz Schimansky-Geier,  Noise in Complex Systems and Stochastic Dynamics, SPIE, 2003, 0-8194-4974-1.- Susan Shannon,  Artificial Intelligence and Computer Science, Nova Science Publishers, 2005, 1-59454-411-5.- Eric W. Weisstein,  CRC Concise Encyclopedia of Mathematics, CRC Press, 2003, 1-58488-347-2.- David Reguera, José M. G. Vilar, and José-Miguel Rubí,  Statistical Mechanics of Biocomplexity, Springer, 1999, 3-540-66245-6.- Sergey M. Bezrukov,  Unsolved Problems of Noise and Fluctuations, Springer, 2003, 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, 1-4020-0077-4.- Tönu Puu and Iryna Sushko,  Business Cycle Dynamics: Models and Tools, Springer, 2006, 3-540-32167-5.- Andrzej S. Nowak and Krzysztof Szajowski,  Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control, Birkhäuser, 2005, 0-8176-4362-1.- Cristel Chandre, Xavier Leoncini, and George M. Zaslavsky,  Chaos, Complexity and Transport: Theory and Applications, World Scientific, 2008, 981-281-879-0.- Richard A. Epstein, The Theory of Gambling and Statistical Logic (Second edition), Academic Press, 2009, 0-12-374940-9.- Clifford A. Pickover,  The Math Book, date=20091003140920  Sterling, 2009, 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 date=20170208005641 -  Parrondo's Paradox - A Simulation date=20230619134201 -  Parrondo's Paradox date=20230301040148  at Futility Closet-  Parrondo's Paradox at Wolfram date=20230501103650 -  Online Parrondo simulator date=20120222131646 -  Parrondo's paradox at Maplesoft date=20211027055333 -  Optimal adaptive strategies and Parrondo- dead-url=no