Dynamic Matching: Experimentation, and Cross-Subsidization

Northwestern University, Evanston IL

Investigators

Abstract

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).