Promotion Design with Path Dependent Network Effects

In many retail settings such as fast-food chains, limited time “collect and win” games are often used to promote products and drive sales to the retail outlets. Unlike the more standard price discount or “buy-X-get-Y” promotional campaigns, the “collect and win” games create short term temporal changes to customers' purchasing behavior - the desire to buy products on promotion and frequency of purchases both increase with the number of previous purchases. We call this the “path dependent network effect” of “collect and win” games. In this paper, we study the promotion design problem for these games, to determine the set of eligible products and the duration of the promotion. This problem is challenging, as the customers' purchasing behavior now depends not only on the product attributes and features (static effect), but also on product eligibility for promotion and historical purchases (path dependent network effect). We model the dynamic choice processes associated with the customers in these games using poissonization of the Polya Urn models, to capture the transient change in the frequency of purchases and purchase probability of each product on promotion. We use this approach to study the optimal promotion design problem under different “collect and win” game settings, by solving non-convex assortment optimization problems. We obtain an exact and/or approximation approach for these problems and show that the revenue-ordered promotion set is already near-optimal in many of these games. The optimal duration then depends on the promotion set chosen, and also on the targeted number of products sold before the game found a winner for the grand prize. Using a set of data provided by a fast-food company which conducts the “collect and win” promotion annually, we show the importance of carefully choosing the promotion set and promotion duration, both decisions that will affect the total revenues and profits generated by such promotion campaigns