双方匹配市场中的最优化及其路径问题

Game theory concerns situations involving conflicting interests of multiple decision makers. Because multiple objectives cannot in general be simultaneously maximized, the optimization results found in other areas of operations and mangement research are largely absent from game theory. But the game-theoretic solutions defined in two-sided market allow the interests of agents on the same side of the market to be simultaneously maximized. Roth studied such kind of optimization and its path in many-to-one market. While the applicant had proven that Roth's claims are incorrect. Thus the study of such kind of optimization and its path in one of the most important branches of game theory, matching theory, is of significant theoretic and pratical meaning. The theoretic basis of such kind of optimization is the stability of the selection matching, the stability of the selection matching endows the set of stable matchings a lattice structure, and the lattice structure of the stable matchings gives the path to the optimal outcomes. This project uses game-theoretic method, with selection matching and lattice as tools, to study the optimization and its path in many-to-one and many-to-many market; solves the stability of many-to-one and many-to-many selection matchings and the lattice structure of many-to-one and many-to-many stable matchings, respectively. Therefore, this project improves and completes the study of optimization and its path in two-sided matching market, and provides underlying theoretic-support and theoretic-basis for market mechanism design and market mangement.

博弈模型涉及多个利益相冲突的决策者。多个目标收益一般难以同时达到最大，所以在博弈论的研究中缺少运筹与管理科学其它领域所取得的最优化结论。但在双方市场中定义的博弈概念，却可以使市场同方参与者的利益同时达到最大；Roth研究了多对一市场中的这种最优化及其路径问题，但申请人证明了Roth的结论是错误的。因此在博弈论最重要的一个理论-匹配理论-中研究最优化及其路径问题，具有重要的理论和现实意义。这种最优化存在的理论依据是选择匹配的稳定性，选择匹配的稳定性赋予稳定匹配集合一定的格结构，稳定匹配集合的格结构给出了达到最优化的具体路径。本项目将以选择匹配和格为工具，用博弈论的分析与证明方法，研究多对一与多对多双方市场的最优化及其路径问题，解决多对一与多对多选择匹配的稳定性及多对一与多对多稳定匹配的格问题。通过研究上述问题，修补并完善了匹配理论的研究，给市场机制设计和市场管理提供有力的理论支撑与理论依据。

在双方市场中定义的博弈概念，可以使市场同方参与者的收益同时达到最大。. 这种最优化存在的理论依据是选择匹配的稳定性。本项目首先用博弈论的分析与证明方法研究多对一双方匹配市场中. 的最优化。在替代偏好和LAD偏好下，证明由企业作选择的选择函数一定是个稳定匹配，由工人做选择的. 选择函数也是一个稳定匹配。 这种最优化存在的理论依据是选择匹配的稳定性，选择匹配的稳定性赋予稳定匹配集合一定的格结构，稳定匹配. 集合的格结构给出了达到最优化的具体路径，其次，本项目用博弈论的分析与证明方法研究多对一双方匹配市场中. 的优化路径，证明稳定匹配集合在Blair偏序下是一个满足分配律的完备格。第三，本项目在笛卡尔单调偏好下，证明了多对多稳定匹配集合是一个满足分配律的完备格。最后，本项目将匹配博弈理论运用到人民币汇率市场，进行了实证研究。