Optimal Dynamic Mechanism Design With Stochastic Supply and Flexible Consumers

In this article, we consider the problem of designing an expected-revenue-maximizing mechanism for allocating multiple nonperishable goods of
$k$
varieties to flexible consumers over
$T$
time steps. In our model, a random number of goods of each variety may become available to the seller at each time, and a random number of consumers may enter the market at each time. Each consumer is present in the market for one time step and wants to consume one good of one of its desired varieties. Each consumer is associated with a flexibility level that indicates the varieties of goods it is equally interested in. A consumer’s flexibility level and the utility it gets from consuming a good of its desired varieties are its private information. We characterize the allocation rule for a Bayesian-incentive-compatible, individually rational, and expected-revenue-maximizing mechanism in terms of the solution to a dynamic program. The corresponding payment function is also specified in terms of the optimal allocation function. We leverage the structure of the consumers’ flexibility model to simplify the dynamic program. Our simplified dynamic program allows us to provide an explicit allocation procedure and a simple payment rule in terms of the solution of the dynamic program.