习近平新时代中国特色社会主义经济思想要求坚持市场在资源配置中起决定性作用，也要求更好发挥政府的作用。匹配理论研究那些不能通过市场和价格机制配置资源的领域，为政府发挥资源配置作用提供了理论依据。随机分配是解决不可分物品公平分配的重要手段，也是匹配理论的重要分支。本项目将匹配理论中的经典机制--首位交换环机制--应用到随机分配问题中。具体地，本项目将结合理论文献和现实问题提出一个随机分配模型，基于禀赋交换的思想和线性规划的方法提出一组随机分配机制，研究这些机制实现效率、公平和其他各种良好性质的条件，并最终探讨如何将这些机制应用于解决包括中小学择校问题和可移植器官如肾脏的交换和分配问题。本项目的创新之处在于：一方面首次将首位交换环机制应用到随机分配问题，解决了若干理论难点，拓展了匹配理论前沿；另一方面观察到现实中广泛存在的复杂禀赋结构，用禀赋交换的思想同时实现了效率和公平，具有重要应用意义。

Xi Jinping's New Century Socialist Economic Thought with Chinese Characteristics requires that the market mechanism should play the crucial role in resource allocation, and at the same time, the government should also play a better role than before. Matching theory is the field of economics that studies areas of resource allocation in which market mechanisms are forbidden. Thus, matching theory provides a theoretical justification for the role of the government and social planners. Random allocation is an important tool to achieve fair allocation of indivisible resource. This project will extend the class mechanism in matching theory--Top Trading Cycle--to random allocation problems. Specifically, this project will propose a random allocation model based on both the literature and real-life problems, propose a class of random mechanisms based on linear programming and the idea of exchanging endowments, study the properties of these mechanisms in efficiency, fairness and other goals, and finally discuss how to apply the mechanisms to solve real-life problems, including school choice and kidney exchange. The innovation of this project includes two respects: first, this project will be the first that extends Top Trading Cycle to random allocation problems, answer several theoretical questions, and thus push forward the frontier of matching theory; second, this project takes account of the widespread rich endowment structure in practice, achieves efficiency and fairness simultaneously based on the idea of endowment exchange, and thus contributes to the application of matching theory.