Theoretical and Empirical Studies on Economic Models with Discrete Structure

在本研究计画中，我们研究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。本研究由理论部分和实证部分两部分组成。在理论研究部分，我们有五篇论文。在第一篇文章中，我们研究了一个具有不可分商品和不对称信息的单边模型。在研究中，我们证明了存在某种均衡，这种均衡在具有无限可分善的模型中不存在。在第二篇文章中，我们利用包括一致性公理在内的一些公理给出了指派问题的核心的一个完整的刻画。这个特征可以解释为一个具有不可分割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，我们研究了具有外部性的匹配问题。我们给出了一个适当的定义的稳定性在这种设置和调查的一些性质的一组稳定的匹配虽然稳定的匹配不一定是帕累托最优的，我们证明存在一个稳定的和帕累托最优的匹配。在第四篇论文中，我们研究了具有不可分割商品的固定价格经济。我们发现，只有一个资源分配机制，满足防策略，帕累托最优，和匿名性。在第五篇论文中，我们研究了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，并发现了一些经验证据表明，一些高中的推荐是由Gale-Shapley算法决定的。我们讨论了一些优点的机制。

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.