Optimal Dynamic Mechanism Design with Stochastic Supply and Flexible Consumers

TL;DR

This paper develops a dynamic mechanism design framework for allocating multiple goods to flexible consumers with stochastic supply and demand, maximizing expected revenue while ensuring incentive compatibility and individual rationality.

Contribution

It introduces a novel dynamic programming approach to characterize optimal mechanisms considering consumer flexibility and stochastic supply/demand.

Findings

Characterizes the optimal allocation rule using a dynamic program.

Simplifies the dynamic program leveraging consumer flexibility structure.

Provides an alternative threshold-based description of the optimal mechanism.

Abstract

We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable 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 the 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 and provide an alternative description of the optimal mechanism in terms of thresholds computed by the dynamic program.