When making a purchase a consumer has a choice between using frequent-flier miles cash or some combination thereof. Which will he or she choose? Another consumer has an opportunity to participate in a special program to get a free car wash after paying for a certain number of washes. What’s the best way for the car-wash owner to motivate the customer to participate? Such questions are serious business for airlines hotel chains credit-card companies and other corporations that offer loyalty programs to customers. Wharton marketing professor Xavier Drèze and Joseph C. Nunes of the University of Southern California’s Marshall School of Business have spent several years studying how these programs can be structured to generate the most revenue for companies offering them.