帕隆多悖论
帕隆多悖论（Parrondo's paradox），是博弈论中的悖论，指一套失败策略的组合反成为获胜策略。 [1] 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，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。[2] 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。[3]
参考 编辑
腳註 编辑
- ^ Harmer, G. P.; Abbott, D. Losing strategies can win by Parrondo's paradox. Nature. 1999, 402 (6764): 864. S2CID 41319393. doi:10.1038/47220
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- ^ 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 ..
延伸阅读 编辑
- 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.
參見 编辑
外部链接 编辑
- 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）.