Bipartite matching model with dynamic arrivals and departures

In this paper, we introduce a bipartite matching model for matching markets with dynamic arrivals and departures. Different from classical models with a finite-time horizon, our model has a long-time horizon with infinite vertices. In our model, the matching goal is to maximize the ratio of matched vertices, i.e., matched ratio. We define two types of online algorithms, i.e., Greedy and Patient, analyze their performance with evaluation metrics of both upper bounds and competitive ratios, and conduct extensive simulations to validate our analysis. To further simulate the real situation, we extend our model with the user’s strategic behavior and prove the existence of a specific Nash equilibrium under a differentiated matching mechanism.

Intertemporal Price Discrimination: Dynamic Arrivals and Changing Values

We study the profit-maximizing price path of a monopolist selling a durable good to buyers who arrive over time and whose values for the good evolve stochastically. The setting is completely stationary with an infinite horizon. Contrary to the case with constant values, optimal prices fluctuate with time. We argue that consumers’ randomly changing values offer an explanation for temporary price reductions that are often observed in practice. (JEL D82)