Dynamic Matching: Experimentation, and Cross-Subsidization

拟议的研究旨在调查市场的动态方面，其中相关方面（例如，工人和公司，或消费者和供应商）之间的互动是由一个或多个平台调解的。这种介导的相互作用通常发生在分散的信息下。例如，只有消费者知道他们对不同供应商的产品和服务的偏好，这意味着这些信息是私有的。同样，工人和公司也有关于潜在合作伙伴价值的私人信息。大多数匹配市场本质上也是动态的，因为匹配值的不确定性逐渐消除，以及改变现有匹配分配的可取性的冲击。例如，一个工人可能会发现她在一段特定关系中的生产力不如预期的那么好，并寻求职业介绍所的帮助来寻找新雇主。一个关键的问题是，在利润最大化和福利最大化的情况下，这种不确定性的渐进和内生解决如何影响匹配分配的动态。为了研究实验和交叉补贴对匹配分配动力学的共同影响，PI计划建立一个将匹配理论元素与动态机制设计元素相结合的模型。平台的问题可以看作是设计一个动态（多对多）匹配机制，指定个体之间的链接如何随着时间的推移而演变，作为匹配值演变的函数。有两个关键的困难：(i)代理的价值是内生的，因为它们反映了过去相互作用的结果；（ii）代理的价值是多维的，因为它们指定了每个代理从每个潜在合作伙伴那里获得的效用。该模型定义了一个具有多维内生类型的动态机制设计问题。或者，平台的问题可以看作是一个强盗问题，在每个时期，决策者（平台）必须拉动多个手臂，这些手臂的回报是代理的私人信息。求解最优匹配分配则需要将动态机制设计的最新文献中的技术（例如，Pavan, Segal, and Toikka, Econometrica, 2014）与运筹学文献中的技术（例如，Gittins, Wiley, 1989）结合起来。

The proposed research aims at investigating dynamic aspects of markets in which the interactions among the relevant sides (e.g., workers and firms, or consumers and vendors) are mediated by one or multiple platforms. Such mediated interactions typically occur under dispersed information. For example, only consumers know about their preferences for the products and services of different vendors meaning this information is private. Similarly workers and firms have private information for their values for potential partners. Most matching markets are also intrinsically dynamic, due to the gradual resolution of uncertainty about matching values, as well as shocks that alter the desirability of the existing matching allocations. For example, a worker may find out that her productivity in a given relationship is not as good as expected and seek the assistance of an employment agency to find a new employer. A key question is then how such gradual and endogenous resolution of uncertainty affects the dynamics of the matching allocations both under profit-maximization and under welfare maximization.To study the joint effects of experimentation and cross-subsidization on the dynamics of the matching allocations, the PI plans to develop a model that combines elements of matching theory with elements of dynamic mechanism design. The platform's problem can be seen as designing a dynamic (many-to-many) matching mechanism specifying how the links among individuals evolve over time as a function of the evolution of the matching values. There are two key difficulties: (i) the agents' values are endogenous, as they reflect the outcomes of past interactions; (ii) the agents' values are multidimensional, as they specify the utilities each agent derives from each potential partner. The model thus defines a dynamic mechanism design problem with multidimensional and endogenous types. Alternatively, the platform's problem can be seen a bandit problem in which, in each period, the decision maker (the platform) must pull multiple arms whose rewards are the agents' private information. Solving for the optimal matching allocations then requires combining techniques from the recent literature on dynamic mechanism design (e.g., Pavan, Segal, and Toikka, Econometrica, 2014) with techniques from the Operation Research literature (e.g., Gittins, Wiley, 1989).