半代数经济模型的均衡点计算:一种代数方法

Computing equilibria of semi-algebraic economies:an algebraic approach

半代数经济模型指的是均衡点可以用半代数系统刻画的经济模型,通常包括静态均衡模型和动态均衡模型两大类.本文介绍了将静态均衡模型的多均衡检测问题以及动态均衡模型的稳定性分析问题转化为半代数系统实解计数问题的一般方法,并针对无参数和带参数两种情形分别提供了分析半代数系统实解个数的系统化算法.与Kubler和Schmedders给出的方法相比,本文介绍的方法考虑了不等式约束,并可以给出均衡点的精确个数.对几个具体的经济模型均衡点的计算分析结果显示了所提算法的有效性.

Semi-algebraic economies are economic models,the equilibria of which could be characterized by semi-algebraic systems.Semi-algebraic economies are usually divided into two classes：static equilibrium models and dynamic equilibrium models.In this paper,we propose general methods to transfer the problems of detecting multiple equilibria in static models and analyzing the stability of equilibria in dynamic models into counting real solutions of semi-algebraic systems.Furthermore,we describe systematic algorithms for computing the number of distinct real solutions of semi-algebraic systems with or without parameters.Compared to the methods by Kubler and Schmedders,ours can better handle models with inequality constraints and can give the precise number of equilibria.The effectiveness of our algorithms is illustrated by the computational results of analyzing a number of specific economic models.