复杂经济学

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此词条由许菁翻译。

25px  此article介紹的是the application of complexity science to the problems of economics。For its application to strategy, see Complexity theory and organizations. For other uses, see Complexity theory (disambiguation).


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Complexity economics is the application of complexity science to the problems of economics. It sees the economy not as a system in equilibrium, but as one in motion, perpetually constructing itself anew.[1][2] It uses computational and mathematical analysis to explore how economic structure is formed and reformed, in continuous interaction with the adaptive behavior of the 'agents' in the economy [3]

Complexity economics is the application of complexity science to the problems of economics. It sees the economy not as a system in equilibrium, but as one in motion, perpetually constructing itself anew. It uses computational and mathematical analysis to explore how economic structure is formed and reformed, in continuous interaction with the adaptive behavior of the 'agents' in the economy

复杂性经济学 Complexity economics是复杂性科学在经济学问题上的应用。它认为经济不是一个处于均衡状态的系统，而是一个处于运动中的系统，不断地重新构建自己。它使用计算和数学分析方法，从经济中的“主体”的适应行为不断相互作用中探索经济结构的形成和变革方式。


模型 Models

The "nearly archetypal example" is an artificial stock market model created by the Santa Fe Institute in 1989.[4] The model shows two different outcomes, one where "agents do not search much for predictors and there is convergence on a homogeneous rational expectations outcome" and another where "all kinds of technical trading strategies appearing and remaining and periods of bubbles and crashes occurring".[4]

The "nearly archetypal example" is an artificial stock market model created by the Santa Fe Institute in 1989. The model shows two different outcomes, one where "agents do not search much for predictors and there is convergence on a homogeneous rational expectations outcome" and another where "all kinds of technical trading strategies appearing and remaining and periods of bubbles and crashes occurring".

这个“近乎典型的例子”是由圣菲研究所在1989年创建的一个人为的股票市场模型。该模型显示了两种不同的结果，一种是”行为主体不太寻找预测因子，而且在同一种理性预期结果上趋于一致”，另一种是”各种技术性交易战略的出现和存在，以及泡沫和崩溃时期的出现”。



Another area has studied the prisoner's dilemma, such as in a network where agents play amongst their nearest neighbors or a network where the agents can make mistakes from time to time and "evolve strategies".[4] In these models, the results show a system which displays "a pattern of constantly changing distributions of the strategies".[4]

Another area has studied the prisoner's dilemma, such as in a network where agents play amongst their nearest neighbors or a network where the agents can make mistakes from time to time and "evolve strategies". In these models, the results show a system which displays "a pattern of constantly changing distributions of the strategies".

另一个领域研究了囚徒困境 Prisoner's Dilemma问题，例如在一个网络中，主体在其最近邻居之间不断活动，或者主体可以不时地犯错并形成“演化策略”。在这些模型中，结果均显示了一个“策略分布模式不断变化”的系统。


More generally, complexity economics models are often used to study how non-intuitive results at the macro-level of a system can emerge from simple interactions at the micro level. This avoids assumptions of the representative agent method, which attributes outcomes in collective systems as the simple sum of the rational actions of the individuals.

More generally, complexity economics models are often used to study how non-intuitive results at the macro-level of a system can emerge from simple interactions at the micro level. This avoids assumptions of the representative agent method, which attributes outcomes in collective systems as the simple sum of the rational actions of the individuals.

更一般地说，复杂经济学模型经常被用来研究系统宏观层面的非直观结果是如何从微观层面的简单相互作用中产生。该方法将集体系统的结果归结为个体理性行为的简单和，避免了代表性主体方法的假设。

方法 Measures

经济复杂性指数 Economic complexity index

MIT physicist César Hidalgo and Harvard economist Ricardo Hausmann introduced a spectral method to measure the complexity of a country's economy by inferring it from the structure of the network connecting countries to the products that they export. The measure combines information of a country's diversity, which is positively correlated with a country's productive knowledge, with measures of a product ubiquity (number of countries that produce or export the product).[5][6] This concept, known as the "Product Space", has been further developed by MIT's Observatory of Economic Complexity, and in The Atlas of Economic Complexity[6] in 2011.

MIT physicist César Hidalgo and Harvard economist Ricardo Hausmann introduced a spectral method to measure the complexity of a country's economy by inferring it from the structure of the network connecting countries to the products that they export. The measure combines information of a country's diversity, which is positively correlated with a country's productive knowledge, with measures of a product ubiquity (number of countries that produce or export the product). This concept, known as the "Product Space", has been further developed by MIT's Observatory of Economic Complexity, and in The Atlas of Economic Complexity in 2011.

麻省理工学院物理学家塞萨尔·伊达尔戈（César Hidalgo）和哈佛大学经济学家里卡多·豪斯曼（Ricardo Hausmann）介绍了一种谱方法，通过各国与出口产品之间的网络结构推断出一个国家经济的复杂性。该指标将与一国生产知识正相关的国家多样性信息与产品普遍性（生产或出口该产品的国家数量）的指标相结合。这个被称为“产品空间”的概念被麻省理工学院的经济复杂性观察站进一步发展，并在2011年的《经济复杂性地图集》中得到了进一步的发展。


相关性 Relevance

The economic complexity index (ECI) introduced by Hidalgo and Hausmann[5][6] is highly predictive of future GDP per capita growth. In Hausmann, Hidalgo et al.,[6] the authors show that the List of countries by future GDP (based on ECI) estimates ability of the ECI to predict future GDP per capita growth is between 5 times and 20 times larger than the World Bank's measure of governance, the World Economic Forum's (WEF) Global Competitiveness Index (GCI) and standard measures of human capital, such as years of schooling and cognitive ability.[7][8]

The economic complexity index (ECI) introduced by Hidalgo and Hausmann is highly predictive of future GDP per capita growth. In Hausmann, Hidalgo et al., the authors show that the List of countries by future GDP (based on ECI) estimates ability of the ECI to predict future GDP per capita growth is between 5 times and 20 times larger than the World Bank's measure of governance, the World Economic Forum's (WEF) Global Competitiveness Index (GCI) and standard measures of human capital, such as years of schooling and cognitive ability.

Hidalgo和Hausmann提出的经济复杂性指数 Economic Complexity Index，ECI对未来人均GDP增长具有很强的预测性。在Hausmann，Hidalgo等人的文章中，作者指出，按未来GDP（基于ECI）列出的国家/地区清单估计，ECI预测未来人均GDP增长的能力是世界银行治理措施的5倍至20倍，也是世界经济论坛（WEF）的全球竞争力指数（GCI）和人力资本的标准衡量标准（如受教育年限和认知能力）的5至20倍。

国家健康状况和产品复杂性指标 Metrics for country fitness and product complexity

Pietronero and collaborators have recently proposed a different approach.[9][10][11] These metrics are defined as the fixed point of non-linear iterative map. Differently from the linear algorithm giving rise to the ECI, this non-linearity is a key point to properly deal with the nested structure of the data. The authors of this alternative formula claim it has several advantages:

Pietronero and collaborators have recently proposed a different approach. These metrics are defined as the fixed point of non-linear iterative map. Differently from the linear algorithm giving rise to the ECI, this non-linearity is a key point to properly deal with the nested structure of the data. The authors of this alternative formula claim it has several advantages:

皮埃特罗内罗（Pietronero）和他的合作者最近提出了一种不同的方法，被定义为非线性迭代映射的不动点。这种非线性特性不同于线性算法，是正确处理数据嵌套结构的关键。作者声称这种替代方法有以下几个优点:


  • Consistency with the empirical evidence from the export country-product matrix that diversification plays a crucial role in the assessment of the competitiveness of countries. The metrics for countries proposed by Pietronero is indeed extensive with respect to the number of products.

与出口国家产品矩阵的经验证据相一致，即多样化在评估国家竞争力中起着至关重要的作用。Pietronero建议的国家/地区指标在产品数量方面确实很广泛。


  • Non-linear coupling between fitness and complexity required by the nested structure of the country-product matrix. The nested structure implies that the information on the complexity of a product must be bounded by the producers with the slowest fitness.

国家产品矩阵的嵌套结构所需的适应性和复杂性之间的非线性耦合。嵌套结构意味着有关产品复杂性的信息必须由适应性最慢的生产者限制。


  • Broad and Pareto-like distribution of the metrics.

指标的广泛分布和帕累托式分布 Pareto Distribution。

  • Each iteration of the method refines information, does not change the meaning of the iterated variables and does not shrink information.

该方法的每次迭代都会精炼信息，但不会更改迭代变量的含义，也不会缩小信息。


The metrics for country fitness and product complexity have been used in a report[12] of the Boston Consulting Group on Sweden growth and development perspectives.

The metrics for country fitness and product complexity have been used in a report of the Boston Consulting Group on Sweden growth and development perspectives.

波士顿咨询集团(Boston Consulting Group)在一份关于瑞典增长和发展前景的报告中使用了国家健康和产品复杂性的衡量标准。

特征 Features

Brian Arthur, Steven N. Durlauf, and David A. Lane describe several features of complex systems that deserve greater attention in economics.[13]

Brian Arthur, Steven N. Durlauf, and David A. Lane describe several features of complex systems that deserve greater attention in economics.

布莱恩 · 亚瑟，史蒂文 · N · 德劳夫和大卫 · A · 莱恩描述了在经济学中值关注的几个复杂系统的特征。


  1. Dispersed interaction—The economy has interaction between many dispersed, heterogeneous, agents. The action of any given agent depends upon the anticipated actions of other agents and on the aggregate state of the economy.
Dispersed interaction—The economy has interaction between many dispersed, heterogeneous, agents. The action of any given agent depends upon the anticipated actions of other agents and on the aggregate state of the economy.

分散的相互作用ーー经济体系中有许多分散的、异质的主体之间的相互作用。任何特定行为主体，其行为取决于其他行为主体的预期行为和经济的总体状况。

  1. No global controller—Controls are provided by mechanisms of competition and coordination between agents. Economic actions are mediated by legal institutions, assigned roles, and shifting associations. No global entity controls interactions. Traditionally, a fictitious auctioneer has appeared in some mathematical analyses of general equilibrium models, although nobody claimed any descriptive accuracy for such models. Traditionally, many mainstream models have imposed constraints, such as requiring that budgets be balanced, and such constraints are avoided in complexity economics.
No global controller—Controls are provided by mechanisms of competition and coordination between agents. Economic actions are mediated by legal institutions, assigned roles, and shifting associations. No global entity controls interactions. Traditionally, a fictitious auctioneer has appeared in some mathematical analyses of general equilibrium models, although nobody claimed any descriptive accuracy for such models.  Traditionally, many mainstream models have imposed constraints, such as requiring that budgets be balanced, and such constraints are avoided in complexity economics.

不存在全局控制器ーー控制是通过主体之间的竞争和协调机制实现的。经济行为是由法律机构、指定的角色和不断变化的协会调解的，而没有全局实体控制交互。尽管没有人在模型描述中准确表达过这一操作，但在一般均衡模型的一些数学分析中通常都会存在一个虚拟的拍卖商。同时传统的许多主流模型都需要施加约束，比如要求预算平衡，但这种约束在复杂性经济学中是非必要的。

  1. Cross-cutting hierarchical organization—The economy has many levels of organization and interaction. Units at any given level behaviors, actions, strategies, products typically serve as "building blocks" for constructing units at the next higher level. The overall organization is more than hierarchical, with many sorts of tangling interactions (associations, channels of communication) across levels.
Cross-cutting hierarchical organization—The economy has many levels of organization and interaction. Units at any given level behaviors, actions, strategies, products typically serve as "building blocks" for constructing units at the next higher level. The overall organization is more than hierarchical, with many sorts of tangling interactions (associations, channels of communication) across levels.

跨领域的层级组织ーー经济具有多层次的组织和互动。任何给定级别的单元行为、动作、策略、产品都会被典型地充当构建下一个更高级别单元的组成要素。整个组织不仅仅是层次结构的，还有许多跨层次的交互(关联、沟通渠道)。

  1. Ongoing adaptation—Behaviors, actions, strategies, and products are revised frequently as the individual agents accumulate experience.[14]
Ongoing adaptation—Behaviors, actions, strategies, and products are revised frequently as the individual agents accumulate experience.

状态的持续改变ー行为、行动、策略和产品随着个体经验的积累而频繁修改。

  1. Novelty niches—Such niches are associated with new markets, new technologies, new behaviors, and new institutions. The very act of filling a niche may provide new niches. The result is ongoing novelty.
Novelty niches—Such niches are associated with new markets, new technologies, new behaviors, and new institutions. The very act of filling a niche may provide new niches. The result is ongoing novelty.

新的商机ーー这些商机可能与新的市场、新的技术、新的行为和新的机构有关。而去满足/填补这些商机这种行为本身就可能提供新的商机。这样的结果就是会不断出现新的商机。

  1. Out-of-equilibrium dynamics—Because new niches, new potentials, new possibilities, are continually created, the economy functions without attaining any optimum or global equilibrium. Improvements occur regularly.
Out-of-equilibrium dynamics—Because new niches, new potentials, new possibilities, are continually created, the economy functions without attaining any optimum or global equilibrium. Improvements occur regularly.

非均衡动态ーー由于新的生态位、新的潜力、新的可能性不断产生，经济运行不会达到任何最佳的或均衡的点。改进是会不断发生的。

当代经济学趋势 Contemporary trends in economics

Complexity economics has a complex relation to previous work in economics and other sciences, and to contemporary economics. Complexity-theoretic thinking to understand economic problems has been present since their inception as academic disciplines. Research has shown that no two separate micro-events are completely isolated,[15] and there is a relationship that forms a macroeconomic structure. However, the relationship is not always in one direction; there is a reciprocal influence when feedback is in operation.[16]

Complexity economics has a complex relation to previous work in economics and other sciences, and to contemporary economics. Complexity-theoretic thinking to understand economic problems has been present since their inception as academic disciplines. Research has shown that no two separate micro-events are completely isolated, and there is a relationship that forms a macroeconomic structure. However, the relationship is not always in one direction; there is a reciprocal influence when feedback is in operation.

复杂性经济学与以往的经济学和其他科学研究以及当代经济学之间都有着复杂的联系。如何利用复杂性理论思维去理解经济这一问题，自其作为一门单独学科学科问世以来就一直存在。研究表明，没有两个独立的微观事件是完全孤立的，它们之间总会存在一种关系，使得最后它们最后会形成一种宏观经济结构。然而，这种关系并不总是朝着一个方向; 当它们之间存在反馈作用时，这种关系之间的影响就是相互的。



Complexity economics has been applied to many fields.

Complexity economics has been applied to many fields.

复杂性经济学已被应用于许多领域。



先行者的智慧 Intellectual predecessors

Complexity economics draws inspiration from behavioral economics, Marxian economics, institutional economics/evolutionary economics, Austrian economics and the work of Adam Smith.[17] It also draws inspiration from other fields, such as statistical mechanics in physics, and evolutionary biology. Some of the 20th century intellectual background of complexity theory in economics is examined in Alan Marshall (2002) The Unity of Nature, Imperial College Press: London. See Douma & Schreuder (2017) for a non-technical introduction to Complexity Economics and a comparison with other economic theories (as applied to markets and organizations).


它也从其他领域获得了灵感，比如物理学中的 http://sandcat.middlebury.edu/econ/repec/mdl/ancoec/0804.pdf 统计力学，以及进化生物学。艾伦•马歇尔(Alan Marshall)2002年出版的《自然的统一》(The Unity of Nature，Imperial College Press: London)探讨了20世纪经济学中复杂性理论的一些知识背景。参见 Douma & Schreuder (2017)对复杂性经济学的非技术性介绍以及与其他经济理论的比较(适用于市场和组织)。



应用 Applications

The theory of complex dynamic systems has been applied in diverse fields in economics and other decision sciences. These applications include capital theory,[18][19] game theory,[20] the dynamics of opinions among agents composed of multiple selves,[21] and macroeconomics.[22] In voting theory, the methods of symbolic dynamics have been applied by Donald G. Saari.[23] Complexity economics has attracted the attention of historians of economics.[24] Ben Ramalingam's Aid on the Edge of Chaos includes numerous applications of complexity economics that are relevant to foreign aid.

The theory of complex dynamic systems has been applied in diverse fields in economics and other decision sciences. These applications include capital theory, game theory, the dynamics of opinions among agents composed of multiple selves, and macroeconomics. In voting theory, the methods of symbolic dynamics have been applied by Donald G. Saari. Complexity economics has attracted the attention of historians of economics. Ben Ramalingam's Aid on the Edge of Chaos includes numerous applications of complexity economics that are relevant to foreign aid.

复杂动态系统理论已经广泛应用于经济学和其他决策科学的各个领域。这些应用包括资本理论、博弈论、由多个自我组成的主体之间的意见动态以及宏观经济学。在投票理论中，符号动力学的方法被 Donald g. Saari 应用。复杂性经济学引起了经济学史家的注意。本 · 拉马林加姆的《在混乱边缘的援助》包括了与外国援助相关的大量复杂经济学的应用。



复杂性经济学是主流，但非正统 Complexity economics as mainstream, but non-orthodox

According to Colander (2000), Colander, Holt & Rosser (2004), and Davis (2008) contemporary mainstream economics is evolving to be more "eclectic",[25][26] diverse,[27][28][29] and pluralistic.[30] Colander, Holt & Rosser (2004) state that contemporary mainstream economics is "moving away from a strict adherence to the holy trinity – rationality, selfishness, and equilibrium", citing complexity economics along with recursive economics and dynamical systems as contributions to these trends.[31] They classify complexity economics as now mainstream but non-orthodox.[32][33]

According to , , and contemporary mainstream economics is evolving to be more "eclectic", diverse, and pluralistic. state that contemporary mainstream economics is "moving away from a strict adherence to the holy trinity – rationality, selfishness, and equilibrium", citing complexity economics along with recursive economics and dynamical systems as contributions to these trends. They classify complexity economics as now mainstream but non-orthodox.

根据，，和当代主流经济学正在演变为更加“折衷” ，多样化和多元化。当代主流经济学正在“从严格遵循神圣的三位一体——理性、自私和均衡” ，引用复杂性经济学、递归经济学和动态系统作为这些趋势的贡献。他们把复杂性经济学归类为现在的主流但非正统。

批评 Criticism

In 1995-1997 publications, Scientific American journalist John Horgan "ridiculed" the movement as being the fourth C among the "failed fads" of "complexity, chaos, catastrophe, and cybernetics".[4] In 1997, Horgan wrote that the approach had "created some potent metaphors: the butterfly effect, fractals, artificial life, the edge of chaos, self organized criticality. But they have not told us anything about the world that is both concrete and truly surprising, either in a negative or in a positive sense."[4][34][35]

In 1995-1997 publications, Scientific American journalist John Horgan "ridiculed" the movement as being the fourth C among the "failed fads" of "complexity, chaos, catastrophe, and cybernetics".

在1995-1997年的出版物中，《科学美国人》记者约翰·霍根（John Horgan）嘲笑该运动是“复杂性、混乱、灾难和控制论”的“失败潮流”中的第四个C。


Rosser "granted" Horgan "that it is hard to identify a concrete and surprising discovery (rather than "mere metaphor") that has arisen due to the emergence of complexity analysis" in the discussion journal of the American Economic Association, the Journal of Economic Perspectives.[4] Surveying economic studies based on complexity science, Rosser wrote that the findings, rather than being surprising, confirmed "already-observed facts."[4] Rosser wrote that there has been "little work on empirical techniques for testing dispersed agent complexity models."[4] Nonetheless, Rosser wrote that "there is a strain of common perspective that has been accumulating as the four C's of cybernetics, catastrophe, chaos, and complexity emerged, which may now be reaching a critical mass in terms of influencing the thinking of economists more broadly."[4]

Rosser "granted" Horgan "that it is hard to identify a concrete and surprising discovery (rather than "mere metaphor") that has arisen due to the emergence of complexity analysis" in the discussion journal of the American Economic Association, the Journal of Economic Perspectives. Surveying economic studies based on complexity science, Rosser wrote that the findings, rather than being surprising, confirmed "already-observed facts." Rosser wrote that there has been "little work on empirical techniques for testing dispersed agent complexity models." Nonetheless, Rosser wrote that "there is a strain of common perspective that has been accumulating as the four C's of cybernetics, catastrophe, chaos, and complexity emerged, which may now be reaching a critical mass in terms of influencing the thinking of economists more broadly."

在美国经济协会的讨论期刊《经济展望》(Journal of Economic Perspectives)上，罗塞(Rosser)“承认”霍根(Horgan)说，由于复杂性分析的出现，很难找到一个具体而令人惊讶的发现(而不仅仅是“隐喻”)。在基于复杂性科学的经济学研究中，罗瑟写道，这些发现不是令人惊讶，而是证实了“已经观察到的事实”罗瑟写道，“在测试分散代理复杂性模型的经验技术方面几乎没有工作。”尽管如此，罗瑟写道，“随着控制论、灾难、混乱和复杂性四个C的出现，有一种共同的观点正在积累，这种观点现在可能已经达到了影响经济学家思维的临界质量。”



参见 See also





注释 Notes

  1. ↑ W. Brian Arthur, Complexity and the Economy, Oxford: Oxford Economic Press, 2015
  2. ↑ Beinhocker, Eric D. The Origin of Wealth: Evolution, Complexity, and the Radical Remaking of Economics. Boston, Massachusetts: Harvard Business School Press, 2006.
  3. ↑ https://www.youtube.com/watch?v=W0dGLEreBrM
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Rosser Jr, J. Barkley (1999). "On the Complexities of Complex Economic Dynamics". Journal of Economic Perspectives. 13 (4): 169–192. doi:10.1257/jep.13.4.169.
  5. ↑ 5.0 5.1 Hidalgo, Cesar A.; Hausmann Ricardo (2009). "The Building Block of Economic Complexity". PNAS. 106 (26): 10570–10575. arXiv:0909.3890. Bibcode:2009PNAS..10610570H. doi:10.1073/pnas.0900943106. PMC 2705545. PMID 19549871.
  6. ↑ 6.0 6.1 6.2 6.3 Hausmann & Hidalgo (2011). The Atlas of Economic Complexity: Mapping Paths to Prosperity. Cambridge, MA: The MIT Press. ISBN 978-0615546629. http://atlas.media.mit.edu/static/pdf/atlas/AtlasOfEconomicComplexity.pdf. 
  7. ↑ "Complexity matters". The Economist. Oct 27, 2011.
  8. ↑ "Diversity Training". The Economist. Feb 4, 2010.
  9. ↑ Tacchella, Andrea; et al. (10 October 2012). "A New Metrics for Countries' Fitness and Products' Complexity". Scientific Reports. 2 (723): 723. Bibcode:2012NatSR...2E.723T. doi:10.1038/srep00723. PMC 3467565. PMID 23056915.
  10. ↑ Cristelli, Matthieu; et al. (2013). "Measuring the Intangibles: A Metrics for the Economic Complexity of Countries and Products". PLOS ONE. 8 (8): e70726. Bibcode:2013PLoSO...870726C. doi:10.1371/journal.pone.0070726. PMC 3733723. PMID 23940633.
  11. ↑ "Economic Complexity: Measuring the Intangibles. A Consumer's Guide" (PDF). Retrieved 30 January 2014.
  12. ↑ "National Strategy for Sweden: From Wealth to Well-being". BCG. Retrieved 30 January 2014.
  13. ↑ Arthur, Brian; Durlauf, Steven; Lane, David A (1997). "Introduction: Process and Emergence in the Economy". The Economy as an Evolving Complex System II. Reading, Mass.: Addison-Wesley. http://www.santafe.edu/~wbarthur/Papers/ADLIntro.html. Retrieved 2008-08-26 
  14. ↑ Shiozawa, Y. (2004). "Evolutionary Economics in the 21st Century: A Manifest". Evolutionary and Institutional Economics Review. 1 (1): 5–47. doi:10.14441/eier.1.5.
  15. ↑ Albert-László Barabási "explaining (at 27:07) that no two events are completely isolated in the BBC Documentary". BBC. Retrieved 11 June 2012. "Unfolding the science behind the idea of six degrees of separation"
  16. ↑ "Page 20 - Ten Principles of Complexity & Enabling Infrastructures" (PDF). by Professor Eve Mitleton-Kelly, Director Complexity Research Programme, London School of Economics. Archived from the original (PDF) on 12 May 2013. Retrieved 1 June 2012.
  17. ↑ Colander, David (March 2008). "Complexity and the History of Economic Thought" (PDF). Retrieved 29 July 2012.
  18. ↑ Rosser Jr, J. Barkley (1983). "Reswitching as a Cusp Catastrophe". Journal of Economic Theory. 31: 182–193. doi:10.1016/0022-0531(83)90029-7.
  19. ↑ Ahmad, Syed Capital in Economic Theory: Neo-classical, Cambridge, and Chaos. Brookfield: Edward Elgar (1991)
  20. ↑ Sato, Yuzuru; Akiyama, Eizo; Farmer, J. Doyne (2002). "Chaos in learning a simple two-person game". Proceedings of the National Academy of Sciences of the United States of America. 99 (7): 4748–4751. Bibcode:2002PNAS...99.4748S. doi:10.1073/pnas.032086299. PMC 123719. PMID 11930020.
  21. ↑ Krause, Ulrich. "Collective Dynamics of Faustian Agents", in Economic Theory and Economic Thought: Essays in honour of Ian Steedman (ed. by John Vint et al.) Routledge: 2010.
  22. ↑ Flaschel, Peter; Proano, Christian R. (2009). "The J2 Status of 'Chaos' in Period Macroeconomics Models". Studies in Nonlinear Dynamics & Econometrics. 13 (2): 2. doi:10.2202/1558-3708.1674. hdl:10419/105911. Archived from the original on 2013-01-17.
  23. ↑ Saari, Donald G. Chaotic Elections: A Mathematician Looks at Voting. American Mathematical Society (2001).
  24. ↑ Bausor, Randall. "Qualitative dynamics in economics and fluid mechanics: a comparison of recent applications", in Natural Images in Economic Thought: Markets Read in Tooth and Claw (ed. by Philip Mirowski). Cambridge: Cambridge University Press (1994).
  25. ↑ "Economists today are not neoclassical according to any reasonable definition of the term. They are far more eclectic, and concerned with different issues than were the economists of the early 1900s, whom the term was originally designed to describe." Colander (2000, p. 130)
  26. ↑ "Modern economics involves a broader world view and is far more eclectic than the neoclassical terminology allows." Colander (2000, p. 133)
  27. ↑ "In our view, the interesting story in economics over the past decades is the increasing variance of acceptable views..." Colander, Holt & Rosser (2004, p. 487)
  28. ↑ "In work at the edge, ideas that previously had been considered central to economics are being modified and broadened, and the process is changing the very nature of economics." Colander, Holt & Rosser (2004, p. 487)
  29. ↑ "When certain members of the existing elite become open to new ideas, that openness allows new ideas to expand, develop, and integrate into the profession... These alternative channels allow the mainstream to expand, and to evolve to include a wider range of approaches and understandings... This, we believe, is already occurring in economics." Colander, Holt & Rosser (2004, pp. 488–489)
  30. ↑ "despite an increasing pluralism on the mainstream economics research frontier..." Davis (2008, p. 353)
  31. ↑ Colander, Holt & Rosser (2004, p. 485)
  32. ↑ "The second (Santa Fe) conference saw a very different outcome and atmosphere than the first. No longer were mainstream economists defensively adhering to general equilibrium orthodoxy... By 1997, the mainstream accepted many of the methods and approaches that were associated with the complexity approach." Colander, Holt & Rosser (2004, p. 497) Colander, Holt & Rosser (2004, pp. 490–492) distinguish between orthodox and mainstream economics.
  33. ↑ Davis (2008, p. 354)
  34. ↑ Horgan, John (1995). "From Complexity to Perplexity". Scientific American. 272 (6): 104–09. Bibcode:1995SciAm.272f.104H. doi:10.1038/scientificamerican0695-104.
  35. ↑ Horgan, John, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. Paperback ed, New York: Broadway Books, 1997.


参考资料 References





  • Rosser, J. Barkley, Jr. From Catastrophe to Chaos: A General Theory of Economic Discontinuities Boston/Dordrecht: Kluwer Academic.


  • Benhabib, Jess (editor) Cycles and Chaos in Economic Equilibrium, Princeton University Press (1992).


  • Waldrop, M. Mitchell. Complexity: The Emerging Science at the Edge of Order and Chaos. New York:Touchstone (1992)


  • Saari, Donald. "Complexity of Simple Economics", Notices of the AMS. V. 42, N. 2 (Feb. 1995): 222-230






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