Theoretical and Empirical Studies on Economic Models with Discrete Structure

在这个研究项目中，我们研究了商品不可分割的经济模型。有两种模型：单边模型和双边模型。本研究项目分为理论部分和实证部分两部分。在理论研究部分，我们有五篇论文。在第一篇论文中，我们研究了一个具有不可分良好信息和不对称信息的单侧模型。在研究中，我们证明了存在某种均衡，这种均衡在无穷可分商品的模型中是不存在的。在第二篇论文中，我们利用包括一致性公理在内的一些公理给出了分配问题核心的完整表征。这种特征可以解释为具有不可分商品的一般均衡模型的一组竞争均衡的特征。在第三篇论文中，我们研究了外部性的匹配问题。在这种情况下，我们给出了稳定性的适当定义，并研究了稳定匹配集的一些性质，尽管稳定匹配不一定是帕累托最优的，但我们证明了存在一个稳定且帕累托最优的匹配。在第四篇论文中，我们研究了商品不可分的固定价格经济。我们证明了只有一种资源分配机制满足策略证明性、帕累托最优性和匿名性。在第五篇论文中，我们研究了一个具有单边外部性的匹配问题。在实证研究方面，我们研究了一个大学录取问题，并找到了一些实证证据，表明某高中的推荐是由Gale-Shapley算法决定的。我们讨论了该机制的一些优点。

In this research project, we study economic models with indivisible goods. There are two kinds of models : one-sided models and two-sided models. This research project consists of two parts : theoretical part and empirical part. In the theoretical research part, we have five papers. In the first paper, we study a one-sided model with indivisible good and asymmetric information. In the research we show that there exists a certain kind of equilibrium that cannot exists in models with infinitely divisible good. In the second paper, we give a complete characterization of the core of assignment problems by using some axioms including a consistency axiom. This characterization can be interpreted as a characterization of a set of competitive equilibria of a general equilibrium model with indivisible goods. In the third paper, we study matching problems with externalities. We give an appropriate definition of stability in this setting and investigate some properties of the set of stable matchinges Although a stable matching in not necessarily Pareto-optimal, we prove that there exists a stable and Pareto-optimal matching. In the fourth paper, we study a fixed-price economy with indivisible good. We show that there is only one resource allocation mechanism that satisfies the strategy-proofness, Pareto-optimality, and anonymity. In the fifth paper, we study a matching problem with one-sided externalities. For the empirical research, we study a college admission problems and we find some empirical evidences which indicate that recommendation by some high school is determined by the Gale-Shapley Algorithm. We discuss some merits of the mechanism.