We consider a classic mechanism design problem in a dynamic environment. The seller (she) seeks to sell a good (or service) to the buyers for recurring consumption. The willingness to pay of each buyer (he) evolves according to a geometric Brownian motion over time and is private information. The arrival time (and departure time) of each buyer is random and private information as well.

The buyer can choose the time at which he enters into a contract with the seller. While he can participate in a contract with the seller immediately upon arrival, he has the option to postpone his participation until a future date. Thus, participation may be progressive over time.
 
The objective of the seller is to find a stationary revenue maximizing mechanism in this dynamic environment. The design of the contract or mechanism is unrestricted and may consist of leasing contracts, sale contracts, or any other form of dynamic contract.