Dynamic Matching Markets and An Application to Residential Real Estate

In the residential real estate market, sellers arrive dynamically over time to put their units up for sale. These assets may differ in their attributes, including location, size, style, acreage, etc. Sellers themselves differ in their own financial constraints, carrying costs, and their delay tolerances, i.e., how long they are willing to wait until they sell their unit. Buyers arrive dynamically over time, differing in their preferences of house attributes, their budgets, and their delay tolerances. Buyer and seller decisions, i.e., how to price, which bid to accept, and whether to wait for better outcomes in the future, depend on the available inventory, its characteristics, the heterogeneity of buyers and sellers, the potential mismatch between buyers and sellers, and their beliefs for potential future arrivals of better units or less patient buyers, etc. This market evolves sequentially, and is subject to other frictions, such as for example the fact that buyers cannot be simultaneously bidding for too many units. This paper studies a microstructure model of this market, explicitly accounting its dynamics and the heterogeneity of buyers, sellers, and inventory. It strives to answer questions such as what explains the fact that similar units sell for different prices; how does the depth of the market depends on the supply and demand imbalance and the buyer and seller preferences; how much faster will a house sell if you lower the price by 5%. The modeling and analysis of a dynamic matching market lies in the interface of the economics literature on market design, the CS/OR literature on matching, the finance/OR literature on market microstructure, and the stochastic networks literature. This paper leverages modeling approaches and tools from each of these areas, as well as the area of quantitative pricing and revenue management. We propose a market microstructure model of such a stochastic and dynamic matching market. We analyze the market dynamics and its equilibrium under the simplifying approximation where buyers and sellers use linear bidding strategies. We characterize steady-state properties such as