帕隆多悖论

帕隆多悖论（'），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，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。

参考
腳註
延伸阅读

• John Allen Paulos, [https://books.google.com/books?id=FUGI7KDTkTUC A Mathematician Plays the Stock Market], Basic Books, 2004, .
• Neil F. Johnson, Paul Jefferies, Pak Ming Hui, [https://books.google.com/books?id=8jfV6nntNPkC&pg=PA74&dq=parrondo Financial Market Complexity*], Oxford University Press, 2003, .
• Ning Zhong and Jiming Liu, [https://books.google.com/books?id=eZ6YCz5NamsC&pg=PA150 Intelligent Agent Technology: Research and Development,] World Scientific, 2001, .
• Elka Korutcheva and Rodolfo Cuerno, [https://books.google.com/books?id=lIoZeb_domwC&pg=PA103 Advances in Condensed Matter and Statistical Physics], Nova Publishers, 2004, .
• Maria Carla Galavotti, Roberto Scazzieri, and Patrick Suppes, [https://books.google.com/books?id=ZuMQAQAAIAAJ&q=parrondo Reasoning, Rationality, and Probability*], Center for the Study of Language and Information, 2008, .
• Derek Abbott and Laszlo B. Kish, [https://books.google.com/books?id=ePoaAQAAIAAJ Unsolved Problems of Noise and Fluctuations], American Institute of Physics, 2000, .
• Visarath In, Patrick Longhini, and Antonio Palacios, [https://books.google.com/books?id=FidKZcUqdIQC&pg=PA307 Applications of Nonlinear Dynamics: Model and Design of Complex Systems], Springer, 2009, .
• Marc Moore, Sorana Froda, and Christian Léger, [https://books.google.com/books?id=SJsDHpgsVgsC&pg=PA185 Mathematical Statistics and Applications: Festschrift for Constance van Eeden], IMS, 2003, .
• Ehrhard Behrends, [https://books.google.com/books?id=liNP2CpsU8EC&pg=PA10 Fünf Minuten Mathematik: 100 Beiträge der Mathematik-Kolumne der Zeitung Die Welt], Vieweg+Teubner Verlag, 2006, .
• Lutz Schimansky-Geier, [https://books.google.com/books?id=WgJTAAAAMAAJ&q=parrondo Noise in Complex Systems and Stochastic Dynamics*], SPIE, 2003, .
• Susan Shannon, [https://books.google.com/books?id=PGtGAAAAYAAJ&q=parrondo Artificial Intelligence and Computer Science*], Nova Science Publishers, 2005, .
• Eric W. Weisstein, [https://books.google.com/books?id=UDk8QARabpwC&pg=PA2152&dq=parrondo CRC Concise Encyclopedia of Mathematics*], CRC Press, 2003, .
• David Reguera, José M. G. Vilar, and José-Miguel Rubí, [https://books.google.com/books?id=0oMp60wubKIC&pg=PA95 Statistical Mechanics of Biocomplexity], Springer, 1999, .
• Sergey M. Bezrukov, [https://books.google.com/books?id=soGS-YcwvxsC&pg=PA82 Unsolved Problems of Noise and Fluctuations], Springer, 2003, .
• Julian Chela-Flores, Tobias C. Owen, and F. Raulin, [https://books.google.com/books?id=q8JwN_1p78UC&pg=PA17&dq=parrondo First Steps in the Origin of Life in the Universe*], Springer, 2001, .
• Tönu Puu and Iryna Sushko, [https://books.google.com/books?id=cTfwjzihuiIC&pg=PA148&dq=parrondo Business Cycle Dynamics: Models and Tools*], Springer, 2006, .
• Andrzej S. Nowak and Krzysztof Szajowski, [https://books.google.com/books?id=l5W20mVBeT4C&pg=PA650&dq=parrondo Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control*], Birkhäuser, 2005, .
• Cristel Chandre, Xavier Leoncini, and George M. Zaslavsky, [https://books.google.com/books?id=md092lhGSOQC&pg=PA107&dq=parrondo Chaos, Complexity and Transport: Theory and Applications*], World Scientific, 2008, .
• Richard A. Epstein, The Theory of Gambling and Statistical Logic (Second edition), Academic Press, 2009, .
• Clifford A. Pickover, [http://sprott.physics.wisc.edu/pickover/math-book.html The Math Book,] Sterling, 2009, .

參見

• 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, [https://web.archive.org/web/20080522013128/http://seneca.fis.ucm.es/parr/GAMES/index.htm Parrondo's paradoxical games]
• [http://www.nature.com/news/1999/991223/full/news991223-13.html Nature news article on Parrondo's paradox]
• [http://www.cut-the-knot.org/ctk/Parrondo.shtml Parrondo's Paradox - A Simulation]
• [http://www.futilitycloset.com/2015/05/27/parrondos-paradox/ Parrondo's Paradox] at Futility Closet
• [https://mathworld.wolfram.com/ParrondosParadox.html Parrondo's Paradox at Wolfram]
• [http://hampshire.edu/lspector/parrondo/parrondo.html Online Parrondo simulator]
• [http://www.maplesoft.com/applications/view.aspx?SID=1761 Parrondo's paradox at Maplesoft]
• [https://web.archive.org/web/20081205004012/http://www.molgen.mpg.de/~rahmann/parrondo/parrondo.shtml Optimal adaptive strategies and Parrondo]

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