Three Assignment Problems

研究议程分为以下几个主题：(1)大分配模型中的完全竞争；(2)创新竞争均衡的效率特性；(3)专业化分工和货币交换。第一部分涉及将有限数量的个体分配到有限数量的位置的基本模型扩展到个体数量和位置都是无限的并且由连续体表示的模型。第二部分将创新问题建模为一个两层分配问题，其中资源（包括可供销售的商品）的分配受到职业选择的影响。第三部分考察了分工的技术优势与分工的技术劣势之间的权衡，即分工对交换技术的要求。对这三个主题的研究可能极其重要。在第一个专题中，拟议的工作可能导致一种新的竞争概念的方法，这种方法将把价格不可操纵和占有代理人的边际贡献等标准作为特殊情况。作业模型作为重要的新理论如线性规划和核心理论发展的实验室有着丰富的历史。这位研究者和他的合作者过去的工作表明，他们对大型分配模型中均衡价格独特性的研究可以为经济理论提供另一种新的、强大的分析工具。第二部分和第三部分应该为以下基本问题提供新的见解：新商品是如何引入的？为什么市场是不完整的？专业化和劳动分工是如何依赖于交换过程或交易技术的？

The research agenda is divided into the following topics: (1) perfect competition in large assignment models; (2) efficiency properties of competitive equilibrium with innovation; and (3) specialization and division of labor and monetary exchange. The first part involves extending the basic model assigning a finite number of individuals to a finite number of positions to one in which the number of individuals and positions are infinite and represented by a continuum. The second part consists of modeling the innovation problem as a two-tiered assignment problem in which the allocation of resources, including the commodities available for sale, is influenced by occupational choices. The third part examines the trade-off between the technological advantages of assignments exhibiting specialization and division of labor and the disadvantages of such assignments in terms of the demands that this places on the technology of exchange. Research on all three topics is potentially extremely important. In the first topic the proposed work could lead to a new way of conceptualizing competition that would capture as special cases such criteria as non manipulability of prices and the appropriation of agents' marginal contributions. The assignment model has a rich history as a laboratory for the development of important new theories such as linear programming and core theory. Past work by the investigator and his collaborators suggests that their study of the uniqueness of equilibrium prices in large assignment models could provide another new, powerful analytical tool for economic theory. The second and third parts should provide new insights into such fundamental questions as: how are new commodities introduced? why are markets incomplete? how does specialization and the division of labor depend on the exchange process, or transaction technology?