Selling Passes to Strategic Customers

Many service providers offer a prepaid package of credits that can be redeemed for future use, often called passes, in conjunction with regular individual sales. In dynamic pricing situations, customers can strategize on the purchase, redemption, and renewal of the pass by optimizing the timing and choices between passes and individual items based on future prices and their own changing needs. In “Selling Passes to Strategic Customers,” Wang, Levin, and Nediak integrate dynamic choice modeling and optimal control theory to study how to jointly price the passes and individual items in a dynamic setting. They endogenize an individual customer’s purchase/redemption decisions in their model and find that the seemingly complex problem has a simple (approximate) solution. The optimal prices remain nearly constant most of the time, except near the beginning and end of the sales horizon, exhibiting so-called turnpike properties. The pass, as a form of advance purchase, allows the seller to capitalize on the customer’s forward-looking behavior by exploiting the uncertainty of customer valuations.