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|description=将整个经济视作不同主体相互作用的动态系统，研究经济的发展过程。
|description=将整个经济视作不同主体相互作用的动态系统，研究经济的发展过程。
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'''<font color="#ff8000">基于主体的计算经济学 Agent-based Computational Economics （ACE）</font>'''是[[计算经济学]]的一个研究领域，将整个经济视作不同主体相互作用的动态系统，研究经济的发展过程。<ref>W. Brian Arthur, 1994. "[https://ocw.tudelft.nl/wp-content/uploads/ElFarolArtur1994.pdf Inductive Reasoning and Bounded Rationality]," ''American Economic Review'', 84(2), pp. [http://www-personal.umich.edu/~samoore/bit885f2011/arthur-inductive.pdf 406-411].<br/> Leigh Tesfatsion, 2003. "Agent-based Computational Economics: Modeling Economies as Complex Adaptive Systems," ''Information Sciences'', 149(4), pp. [http://copper.math.buffalo.edu/urgewiki/uploads/Literature/Tesfatsion2002.pdf 262-268] {{webarchive|url=https://web.archive.org/web/20120426000037/http://copper.math.buffalo.edu/urgewiki/uploads/Literature/Tesfatsion2002.pdf |date=26 April 2012 }}.</ref>
'''<font color="#ff8000">基于主体的计算经济学 Agent-based Computational Economics （ACE）</font>'''是[[计算经济学]]的一个研究领域，将整个经济视作不同主体相互作用的动态系统，研究经济的发展过程。<ref>W. Brian Arthur, 1994. "[https://ocw.tudelft.nl/wp-content/uploads/ElFarolArtur1994.pdf Inductive Reasoning and Bounded Rationality]," ''American Economic Review'', 84(2), pp. [http://www-personal.umich.edu/~samoore/bit885f2011/arthur-inductive.pdf 406-411].</ref><ref>Leigh Tesfatsion, 2003. "Agent-based Computational Economics: Modeling Economies as Complex Adaptive Systems," ''Information Sciences'', 149(4), pp. [http://copper.math.buffalo.edu/urgewiki/uploads/Literature/Tesfatsion2002.pdf 262-268].</ref>
因此，它属于[[复杂适应系统]]的科学范式。在相应的[[基于主体模型]]中，“主体”指根据特定规则进行交互的计算实体，而非真实的人。其中交互的规则一种对个体行为和社会互动的建模。<ref>Scott E. Page (2008). "agent-based models," ''The New Palgrave Dictionary of Economics]'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_A000218&edition=current&q=agent-based%20computational%20modeling&topicid=&result_number=1 Abstract].</ref>
因此，它属于[[复杂适应系统]]的科学范式。在相应的[[基于主体模型]]中，“主体”指根据特定规则进行交互的计算实体，而非真实的人。其中交互的规则一种对个体行为和社会互动的建模。<ref>Scott E. Page (2008). "agent-based models," ''The New Palgrave Dictionary of Economics]'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_A000218&edition=current&q=agent-based%20computational%20modeling&topicid=&result_number=1 Abstract].</ref>
这些规则甚至可以通过人工智能方法（如'''<font color="#ff8000">Q学习 Q-learning</font>'''及其他强化学习技术）来获得。<ref>Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, The MIT Press, Cambridge, MA, 1998 [http://www.cs.ualberta.ca/~sutton/book/ebook/the-book.html] {{Webarchive|url=https://web.archive.org/web/20090904194934/http://www.cs.ualberta.ca/~sutton/book/ebook/the-book.html |date=4 September 2009 }}</ref>
这些规则甚至可以通过人工智能方法（如'''<font color="#ff8000">Q学习 Q-learning</font>'''及其他强化学习技术）来获得。<ref>Richard S. Sutton and Andrew G. Barto, Reinforcement Learning: An Introduction, The MIT Press, Cambridge, MA, 1998 [http://www.cs.ualberta.ca/~sutton/book/ebook/the-book.html] </ref>
传统经济学中个体会理性地计算均衡状态地理论假设被舍弃，取而代之地是更为宽松、现实地假设——个体的理性有限，且其行为仅仅是对市场变化做出适应（而非计算均衡）。<ref>John H. Hollandand John H. Miller (1991). "Artificial Adaptive Agents in Economic Theory," ''American Economic Review'', 81(2), pp. [http://www.santafe.edu/media/workingpapers/91-05-025.pdf 365-370] {{Webarchive|url=https://web.archive.org/web/20110105015853/http://www.santafe.edu/media/workingpapers/91-05-025.pdf |date=5 January 2011 }} p. 366.<br/> Thomas C. Schelling(1978 [2006]). ''Micromotives and Macrobehavior'', Norton. [http://books.wwnorton.com/books/978-0-393-32946-9/ Description] {{Webarchive|url=https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ |date=2 November 2017 }}, [https://books.google.com/books?id=DenWKRgqzWMC&printsec=find&pg=PA1=#v=onepage&q&f=false preview].<br/> Thomas J. Sargent, 1994. ''Bounded Rationality in Macroeconomics'', Oxford. [http://www.oup.com/us/catalog/general/subject/Economics/MacroeconomicTheory/?view=usa&ci=9780198288695 Description] and chapter-preview 1st-page [https://www.questia.com/library/book/bounded-rationality-in-macroeconomics-thomas-j-sargent-by-thomas-j-sargent.jsp links.]</ref>基于主体的计算经济学模型（ACE）将数值分析方法应用于复杂动力学问题，进行计算机模拟，这种方法可以应对传统方法，如数学方程不适用的问题。<ref>Kenneth L. Judd, 2006. "Computationally Intensive Analyses in Economics," ''Handbook of Computational Economics'', v. 2, ch. 17, Introduction, p. 883. [Pp. [https://books.google.com/books?id=6ITfRkNmKQcC&pg=PA881 881-] 893. Pre-pub [https://www2.econ.iastate.edu/tesfatsi/Judd.finalrev.pdf PDF].
传统经济学中个体会理性地计算均衡状态地理论假设被舍弃，取而代之地是更为宽松、现实地假设——个体的理性有限，且其行为仅仅是对市场变化做出适应（而非计算均衡）。<ref>John H. Hollandand John H. Miller (1991). "Artificial Adaptive Agents in Economic Theory," ''American Economic Review'', 81(2), pp. [http://www.santafe.edu/media/workingpapers/91-05-025.pdf 365-370] p. 366.</ref><ref>Thomas C. Schelling(1978 [2006]). ''Micromotives and Macrobehavior'', Norton. [http://books.wwnorton.com/books/978-0-393-32946-9/ Description] ,[https://books.google.com/books?id=DenWKRgqzWMC&printsec=find&pg=PA1=#v=onepage&q&f=false preview].</ref><ref>Thomas J. Sargent, 1994. ''Bounded Rationality in Macroeconomics'', Oxford. [http://www.oup.com/us/catalog/general/subject/Economics/MacroeconomicTheory/?view=usa&ci=9780198288695 Description] and chapter-preview 1st-page [https://www.questia.com/library/book/bounded-rationality-in-macroeconomics-thomas-j-sargent-by-thomas-j-sargent.jsp links.]</ref>基于主体的计算经济学模型（ACE）将数值分析方法应用于复杂动力学问题，进行计算机模拟，这种方法可以应对传统方法，如数学方程不适用的问题。<ref>Kenneth L. Judd, 2006. "Computationally Intensive Analyses in Economics," ''Handbook of Computational Economics'', v. 2, ch. 17, Introduction, p. 883. [Pp. [https://books.google.com/books?id=6ITfRkNmKQcC&pg=PA881 881-] 893. Pre-pub [https://www2.econ.iastate.edu/tesfatsi/Judd.finalrev.pdf PDF].
</ref>\从建模者指定的初始条件开始，计算经济学模型会随着时间的推移而不断演化，模型中的主体不断地对其他参与者交互，包括从交互中学习。在这个角度来看，ACE 被认为是一种自下而上研究经济系统的方法。<ref>Leigh Tesfatsion (2002). "Agent-Based Computational Economics: Growing Economies from the Bottom Up," ''Artificial Life'', 8(1), pp.55-82. [http://www.mitpressjournals.org/doi/abs/10.1162/106454602753694765 Abstract] and pre-pub [http://www.econ.brown.edu/fac/Peter_Howitt/SummerSchool/Agent.pdf PDF]</ref>
ACE 与博弈论时有相似之处和重叠部分，都可以看作以一种研究社会交往的基于主体的建模方法。<ref name="COMP>">Joseph Y. Halpern(2008). "computer science and game theory," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_C000566&edition=current&q=&topicid=&result_number=1 Abstract].<br/> • Yoav Shoham (2008). "Computer Science and Game Theory," ''Communications of the ACM'', 51(8), pp.
ACE 与博弈论时有相似之处和重叠部分，都可以看作以一种研究社会交往的基于主体的建模方法。<ref name="COMP>">Joseph Y. Halpern(2008). "computer science and game theory," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_C000566&edition=current&q=&topicid=&result_number=1 Abstract].<br/> • Yoav Shoham (2008). "Computer Science and Game Theory," ''Communications of the ACM'', 51(8), pp.
[http://www.robotics.stanford.edu/~shoham/www%20papers/CSGT-CACM-Shoham.pdf 75-79] {{Webarchive|url=https://web.archive.org/web/20120426005917/http://www.robotics.stanford.edu/~shoham/www%20papers/CSGT-CACM-Shoham.pdf |date=26 April 2012 }}.<br/> • [[Alvin E. Roth]] (2002). "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," ''Econometrica'', 70(4), pp. [https://web.archive.org/web/20040414102216/http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf 1341–1378].</ref> 但实践者也注意到了ACE与标准的博弈论方法的区别，例如，在ACE中，事件仅由初始条件驱动；ACE不在乎计算上是否易于处理；ACE中，主体有自动选择和学习的能力。<ref>Tesfatsion, Leigh (2006), "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, ''Handbook of Computational Economics'', v. 2, part 2, ACE study of economic system. [http://www.sciencedirect.com/science/article/pii/S1574002105020162 Abstract] and pre-pub [http://econ2.econ.iastate.edu/tesfatsi/hbintlt.pdf PDF].</ref>
[http://www.robotics.stanford.edu/~shoham/www%20papers/CSGT-CACM-Shoham.pdf 75-79] .</ref><ref>Alvin E. Roth (2002). "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," ''Econometrica'', 70(4), pp. [https://web.archive.org/web/20040414102216/http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf 1341–1378].</ref> 但实践者也注意到了ACE与标准的博弈论方法的区别，例如，在ACE中，事件仅由初始条件驱动；ACE不在乎计算上是否易于处理；ACE中，主体有自动选择和学习的能力。<ref>Tesfatsion, Leigh (2006), "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, ''Handbook of Computational Economics'', v. 2, part 2, ACE study of economic system. [http://www.sciencedirect.com/science/article/pii/S1574002105020162 Abstract] and pre-pub [http://econ2.econ.iastate.edu/tesfatsi/hbintlt.pdf PDF].</ref>
得益于计算机科学建模技术的不断改进和计算机能力的提高，ACE方法也在不断发展，其终极科学目标是“用实际数据来检验理论发现——使得可靠的、有实际经验和数据支撑的理论能不断积累，而研究人员也能在可靠的前人理论基础上做进一步探索。”<ref>Leigh Tesfatsion (2006). "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, ''Handbook of Computational Economics'', v. 2, [pp. 831-880] sect. 5. [http://www.sciencedirect.com/science/article/pii/S1574002105020162 Abstract] and pre-pub [http://econ2.econ.iastate.edu/tesfatsi/hbintlt.pdf PDF].<br/> • [[Kenneth L. Judd]] (2006). "Computationally Intensive Analyses in Economics," ''Handbook of Computational Economics'', v. 2, ch. 17, pp. [https://books.google.com/books?id=6ITfRkNmKQcC&pg=PA881 881-] 893. Pre-pub [https://www2.econ.iastate.edu/tesfatsi/Judd.finalrev.pdf PDF].<br/> Leigh Tesfatsion and Kenneth L. Judd, ed. (2006). ''Handbook of Computational Economics'', v. 2. [http://www.elsevier.com/wps/find/bookdescription.cws_home/660847/description#description Description] {{Webarchive|url=https://web.archive.org/web/20120306100156/http://www.elsevier.com/wps/find/bookdescription.cws_home/660847/description#description |date=6 March 2012 }} & and chapter-preview
得益于计算机科学建模技术的不断改进和计算机能力的提高，ACE方法也在不断发展，其终极科学目标是“用实际数据来检验理论发现——使得可靠的、有实际经验和数据支撑的理论能不断积累，而研究人员也能在可靠的前人理论基础上做进一步探索。”<ref>Leigh Tesfatsion (2006). "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, ''Handbook of Computational Economics'', v. 2, [pp. 831-880] sect. 5. [http://www.sciencedirect.com/science/article/pii/S1574002105020162 Abstract] and pre-pub [http://econ2.econ.iastate.edu/tesfatsi/hbintlt.pdf PDF].<br/> </ref><ref>Kenneth L. Judd (2006). "Computationally Intensive Analyses in Economics," ''Handbook of Computational Economics'', v. 2, ch. 17, pp. [https://books.google.com/books?id=6ITfRkNmKQcC&pg=PA881 881-] 893. Pre-pub [https://www2.econ.iastate.edu/tesfatsi/Judd.finalrev.pdf PDF].<br/> Leigh Tesfatsion and Kenneth L. Judd, ed. (2006). ''Handbook of Computational Economics'', v. 2. [http://www.elsevier.com/wps/find/bookdescription.cws_home/660847/description#description Description] & and chapter-preview
[http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574002105X02003&_cid=273377&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=e4757b4f65755ed6340a11fee9615200 links.]</ref>现在，ACE方法已应用于如资产定价、<ref name=arthuretal>B. Arthur, J. Holland, B. LeBaron, R. Palmer, P. Taylor (1997), 'Asset pricing under endogenous expectations in an artificial stock market,' in ''The Economy as an Evolving Complex System II'', B. Arthur, S. Durlauf, and D. Lane, eds., Addison Wesley.</ref>竞争与合作、<ref>Robert Axelrod (1997). ''The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration'', Princeton. [http://press.princeton.edu/titles/6144.html Description], [http://press.princeton.edu/titles/6144.html#TOC contents], and [https://books.google.com/books?id=J0dgRGMdjmQC&printsec=find&pg=PR11#v=onepage&q&f=false preview].</ref> '''<font color="#ff8000">交易成本 Transaction Cost</font>'''、<ref>Tomas B. Klosa and Bart Nooteboom, 2001. "Agent-based Computational Transaction Cost Economics," ''Journal of Economic Dynamics and Control'' 25(3–4), pp. 503–52. [http://www.sciencedirect.com/science/article/pii/S0165188900000348 Abstract.]</ref>市场形式与'''<font color="#ff8000">产业组织 Industrial Organization</font>'''与动态、<ref>Roberto Leombruni and Matteo Richiardi, ed. (2004), ''Industry and Labor Dynamics: The Agent-Based Computational Economics Approach.'' World Scientific Publishing {{ISBN|981-256-100-5}}. [http://www.worldscibooks.com/economics/5706.html Description] and chapter-preview [https://books.google.com/books?id=P5O7A5D55nQC&printsec=fond&pg=PR5#v=onepage&q&f=false links].<br/> • [[Joshua M. Epstein]] (2006). "Growing Adaptive Organizations: An Agent-Based Computational Approach," in ''Generative Social Science: Studies in Agent-Based Computational Modeling'', pp. [https://books.google.com/books?id=543OS3qdxBYC&pg=PA309 309-] 344. [http://press.princeton.edu/titles/8277.html Description] and [http://www.santafe.edu/research/working-papers/abstract/99895b6465e8b87656612f8e3570b34c/ abstract].</ref>'''<font color="#ff8000">福利经济学 Welfare Economics</font>'''、<ref>Robert Axtell (2005). "The Complexity of Exchange," ''Economic Journal'', 115(504, Features), pp. [http://econfaculty.gmu.edu/pboettke/workshop/archives/f05/Axtell.pdf F193-F210].</ref> '''<font color="#ff8000">机制设计 Mechanism Design</font>'''、 <ref>• ''The New Palgrave Dictionary of Economics'' (2008), 2nd Edition: <br/> [[Roger B. Myerson]] "mechanism design." [http://www.dictionaryofeconomics.com/article?id=pde2008_M000132&edition=current&q=mechanism%20design&topicid=&result_number=3 Abstract.] <br/> _____. "revelation principle." [http://www.dictionaryofeconomics.com/article?id=pde2008_R000137&edition=current&q=moral&topicid=&result_number=1 Abstract.]<br/> Tuomas Sandholm. "computing in mechanism design." [http://www.dictionaryofeconomics.com/article?id=pde2008_C000563&edition=&field=keyword&q=algorithmic%20mechanism%20design&topicid=&result_number=1 Abstract.]</ref><ref> Noam Nisan and Amir Ronen (2001). "Algorithmic Mechanism Design," ''Games and Economic Behavior'', 35(1-2), pp. [https://www.cs.cmu.edu/~sandholm/cs15-892F09/Algorithmic%20mechanism%20design.pdf 166–196].<br/> Noam Nisan ''et al''., ed. (2007). ''Algorithmic Game Theory'', Cambridge University Press. [http://www.cup.cam.ac.uk/asia/catalogue/catalogue.asp?isbn=9780521872829 Description] .</ref>信息与不确定性、<ref>Tuomas W. Sandholm and Victor R. Lesser (2001). "Leveled Commitment Contracts and Strategic Breach," ''Games and Economic Behavior'', 35(1-2), pp. [https://www.cs.cmu.edu/afs/.cs.cmu.edu/Web/People/sandholm/leveled.geb.pdf 212-270].</ref> '''<font color="#ff8000">宏观经济学 Macroeconomics</font>'''<ref>David Colander, Peter Howitt, Alan Kirman, Axel Leijonhufvud, and Perry Mehrling, 2008. "Beyond DSGE Models: Toward an Empirically Based Macroeconomics," ''American Economic Review'', 98(2), pp. [https://www.jstor.org/pss/29730026 236]-240. Pre-pub [http://www.brown.edu/Departments/Economics/Faculty/Peter_Howitt/publication/complex%20macro6.pdf PDF].<br/> </ref><ref>Thomas J. Sargent(1994). ''Bounded Rationality in Macroeconomics'', Oxford. [http://www.oup.com/us/catalog/general/subject/Economics/MacroeconomicTheory/?view=usa&ci=9780198288695 Description] and chapter-preview 1st-page [https://www.questia.com/library/book/bounded-rationality-in-macroeconomics-thomas-j-sargent-by-thomas-j-sargent.jsp links].<br/> M. Oeffner (2009). '[http://www.opus-bayern.de/uni-wuerzburg/volltexte/2009/3927/pdf/OeffnerDissohneAnhang.pdf Agent-based Keynesian Macroeconomics]'. PhD thesis, Faculty of Economics, University of Würzburg.</ref>和'''<font color="#ff8000">马克思主义政治经济学 Marxist economics</font>'''<ref>A. F. Cottrell, P. Cockshott, G. J. Michaelson, I. P. Wright, V. Yakovenko
(2009), ''Classical Econophysics''. Routledge, {{ISBN|978-0-415-47848-9}}.</ref><ref>Leigh Tesfatsion (2006), "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, ''Handbook of Computational Economics'', v. 2, part 2, ACE study of economic system. [http://www.sciencedirect.com/science/article/pii/S1574002105020162 Abstract] and pre-pub [http://econ2.econ.iastate.edu/tesfatsi/hbintlt.pdf PDF].</ref>等研究领域。
(2009), ''Classical Econophysics''. Routledge, {{ISBN|978-0-415-47848-9}}.</ref><ref>Leigh Tesfatsion (2006), "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, ''Handbook of Computational Economics'', v. 2, part 2, ACE study of economic system. [http://www.sciencedirect.com/science/article/pii/S1574002105020162 Abstract] and pre-pub [http://econ2.econ.iastate.edu/tesfatsi/hbintlt.pdf PDF].</ref>等研究领域。
==概述==
==概述==
ACE 模型中的“主体（agent）”可以代表个体（如人）、社会群体（如公司）、生物实体（如生长中的庄稼）和/或物理系统（如运输系统），整个ACE模型就是由多个相互作用的主体组成的计算经济系统。建模者首先为ACE模型设置初始参数。然后，ACE模型就会自行演化，建模人员则观察系统随着时间的推移而演化的情况，不需要做进一步的干预。注意，系统活动应由主体间的相互作用驱动，而不需要外部强加平衡条件。<ref>[http://www.socsci.aau.dk/ae2006/ Summary of methods] {{Webarchive|url=https://web.archive.org/web/20070526105550/http://www.socsci.aau.dk/ae2006/ |date=26 May 2007 }}: ''Department of Economics, Politics and Public Administration, Aalborg University, Denmark'' website.</ref>目前来说，ACE面临的研究问题包括所有'''<font color="#ff8000">实验经济学 Experimental economics</font>'''会遇到的普遍问题，以及开发用于验证模型正确性的的通用框架，和其他基于主体的建模中尚未解决的开放问题。<ref>[[Vernon L. Smith]], 2008. "experimental economics," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_E000277&q=experimental%20&topicid=&result_number=2 Abstract].</ref> and development of a common framework for empirical validation and resolving open questions in agent-based modeling.<ref>Giorgio Fagiolo, Alessio Moneta, and Paul Windrum, 2007. "A Critical Guide to Empirical Validation of Agent-Based Models in Economics: Methodologies, Procedures, and Open Problems," ''Computational Economics'', 30, pp. [https://doi.org/10.1007%2Fs10614-007-9104-4 195]–226.</ref>
ACE 模型中的“主体（agent）”可以代表个体（如人）、社会群体（如公司）、生物实体（如生长中的庄稼）和/或物理系统（如运输系统），整个ACE模型就是由多个相互作用的主体组成的计算经济系统。建模者首先为ACE模型设置初始参数。然后，ACE模型就会自行演化，建模人员则观察系统随着时间的推移而演化的情况，不需要做进一步的干预。注意，系统活动应由主体间的相互作用驱动，而不需要外部强加平衡条件。<ref>[http://www.socsci.aau.dk/ae2006/ Summary of methods]: ''Department of Economics, Politics and Public Administration, Aalborg University, Denmark'' website.</ref>目前来说，ACE面临的研究问题包括所有'''<font color="#ff8000">实验经济学 Experimental economics</font>'''会遇到的普遍问题，<ref>Vernon L. Smith, 2008. "experimental economics," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_E000277&q=experimental%20&topicid=&result_number=2 Abstract].</ref>以及开发用于验证模型正确性的的通用框架，和其他基于主体的建模中尚未解决的开放问题。<ref>Giorgio Fagiolo, Alessio Moneta, and Paul Windrum, 2007. "A Critical Guide to Empirical Validation of Agent-Based Models in Economics: Methodologies, Procedures, and Open Problems," ''Computational Economics'', 30, pp. [https://doi.org/10.1007%2Fs10614-007-9104-4 195]–226.</ref>