经济学中均衡的计算及其在排序机制中的应用

项目名称： 经济学中均衡的计算及其在排序机制中的应用

项目编号： No.11501464

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 杜野

作者单位： 西南财经大学

项目金额： 18万元

中文摘要： 纳什均衡和一般均衡是微观经济学中的重要概念。它们被广泛地应用于解释和预测个人和经济体的行为。John Nash, Kenneth Arrow和Gerald Debreu由于证明了纳什均衡和一般均衡的存在性分别获得诺贝尔经济学奖。但是他们的证明都不是构造性的，如何有效地计算经济学中的均衡一直是经济学领域重要的未完善解决的问题。研究经济学中均衡的计算，为运筹学，特别是最优化理论的发展，提出了新的挑战，同时也为最优化理论提供了新的应用平台和前景。本课题拟进行三个方面的研究：1）具有常数替代弹性系数(CES)效用函数的Arrow-Debreu经济体一般均衡的计算；2）两个局中人非合作博弈的近似纳什均衡的计算；3）一般均衡在排名机制中的应用。本课题的研究成果可以丰富最优化理论和算法理论，并且增强微观经济理论的实用性。

中文关键词： 均衡计算；排序博弈；算法机制设计

英文摘要： Nash equilibrium and general equilibrium are two of the most important concepts in microeconomics. They are used to understand and predict the behaviors of rational individuals as well as economies. Because of their contributions to prove the existence of economic equilibrium, John Nash, Kenneth Arrow and Gerald Debreu were awarded the Nobel Prize for Economics separately. However, their proofs of the existence of economic equilibrium are non-constructive；moreover,the problem of efficient equilibria computation is far from well studied. The study of economic equilibrium computation not only poses new challenges to operations research, in particular the optimization theories, but also provides new applications frontiers for optimization theories. In this project, three categories of problems will be investigated: 1)the computation of Arrow-Debreu equilibrium of an economy with CES utilities; 2)the computation of approximate nash equilibrium in bimatrix games; 3)the application of general equilibrium theory in ranking mechanism. This project will make substantial contributions to advancing optimization and algorithm theories, and to making microeconomic theories more practical as well.

英文关键词： equilibrium computation;ranking game;algorithmic mechanism design