英文标题：
《Singularities and Catastrophes in Economics: Historical Perspectives and
  Future Directions》
---
作者：
Michael S. Harr\\\'e and Adam Harris and Scott McCallum
---
最新提交年份：
2019
---
英文摘要：
  Economic theory is a mathematically rich field in which there are opportunities for the formal analysis of singularities and catastrophes. This article looks at the historical context of singularities through the work of two eminent Frenchmen around the late 1960s and 1970s. Ren\\\'e Thom (1923-2002) was an acclaimed mathematician having received the Fields Medal in 1958, whereas G\\\'erard Debreu (1921-2004) would receive the Nobel Prize in economics in 1983. Both were highly influential within their fields and given the fundamental nature of their work, the potential for cross-fertilisation would seem to be quite promising. This was not to be the case: Debreu knew of Thom\'s work and cited it in the analysis of his own work, but despite this and other applied mathematicians taking catastrophe theory to economics, the theory never achieved a lasting following and relatively few results were published. This article reviews Debreu\'s analysis of the so called ${\\it regular}$ and ${\\it crtitical}$ economies in order to draw some insights into the economic perspective of singularities before moving to how singularities arise naturally in the Nash equilibria of game theory. Finally a modern treatment of stochastic game theory is covered through recent work on the quantal response equilibrium. In this view the Nash equilibrium is to the quantal response equilibrium what deterministic catastrophe theory is to stochastic catastrophe theory, with some caveats regarding when this analogy breaks down discussed at the end.
---
中文摘要：
经济理论是一个数学丰富的领域，其中有机会对奇点和灾难进行形式化分析。本文通过20世纪60年代末和70年代左右两位杰出法国人的作品来审视奇点的历史背景。勒内·托姆（1923-2002）是一位备受赞誉的数学家，曾于1958年获得菲尔兹奖，而杰拉德·德布鲁（1921-2004）将于1983年获得诺贝尔经济学奖。两者在各自领域内都具有很高的影响力，鉴于其工作的基本性质，杂交受精的潜力似乎相当大。事实并非如此：德布鲁知道托马斯的工作，并在分析自己的工作时引用了他的工作，但尽管他和其他应用数学家将突变理论引入经济学，但该理论从未获得持久的关注，发表的结果也相对较少。本文回顾了Debreu对所谓的${\\it regular}$和${\\it critical}$经济体的分析，以便在探讨奇点如何在博弈论的纳什均衡中自然产生之前，对奇点的经济观点有一些见解。最后，通过最近对量子响应均衡的研究，介绍了随机博弈论的现代处理方法。在这种观点下，纳什均衡对量子响应均衡的影响就像确定性突变理论对随机突变理论的影响一样，最后讨论了关于这种类比何时失效的一些注意事项。
---
分类信息：

一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
--
一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
--

---
PDF下载：
-->