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, A Mathematician Plays the Stock Market, Basic Books, 2004, .
 Neil F. Johnson, Paul Jefferies, Pak Ming Hui, Financial Market Complexity, Oxford University Press, 2003, .
 Ning Zhong and Jiming Liu, Intelligent Agent Technology: Research and Development, World Scientific, 2001, .
 Elka Korutcheva and Rodolfo Cuerno, Advances in Condensed Matter and Statistical Physics, Nova Publishers, 2004, .
 Maria Carla Galavotti, Roberto Scazzieri, and Patrick Suppes, Reasoning, Rationality, and Probability, Center for the Study of Language and Information, 2008, .
 Derek Abbott and Laszlo B. Kish, Unsolved Problems of Noise and Fluctuations, American Institute of Physics, 2000, .
 Visarath In, Patrick Longhini, and Antonio Palacios, Applications of Nonlinear Dynamics: Model and Design of Complex Systems, Springer, 2009, .
 Marc Moore, Sorana Froda, and Christian Léger, Mathematical Statistics and Applications: Festschrift for Constance van Eeden, IMS, 2003, .
 Ehrhard Behrends, Fünf Minuten Mathematik: 100 Beiträge der Mathematik-Kolumne der Zeitung Die Welt, Vieweg+Teubner Verlag, 2006, .
 Lutz Schimansky-Geier, Noise in Complex Systems and Stochastic Dynamics, SPIE, 2003, .
 Susan Shannon, Artificial Intelligence and Computer Science, Nova Science Publishers, 2005, .
 Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 2003, .
 David Reguera, José M. G. Vilar, and José-Miguel Rubí, Statistical Mechanics of Biocomplexity, Springer, 1999, .
 Sergey M. Bezrukov, Unsolved Problems of Noise and Fluctuations, Springer, 2003, .
 Julian Chela-Flores, Tobias C. Owen, and F. Raulin, First Steps in the Origin of Life in the Universe, Springer, 2001, .
 Tönu Puu and Iryna Sushko, Business Cycle Dynamics: Models and Tools, Springer, 2006, .
 Andrzej S. Nowak and Krzysztof Szajowski, Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control, Birkhäuser, 2005, .
 Cristel Chandre, Xavier Leoncini, and George M. Zaslavsky, 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, 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, Parrondo's paradoxical games
 Nature news article on Parrondo's paradox 
 Parrondo's Paradox - A Simulation 
 Parrondo's Paradox  at Futility Closet
 Parrondo's Paradox at Wolfram 
 Online Parrondo simulator 
 Parrondo's paradox at Maplesoft 
 Optimal adaptive strategies and Parrondo

Category:决策悖论
Category:博弈论
Category:数学悖论