Overbooking with Endogenous Demand

Using airlines as a backdrop, we study optimal overbooking policies with endogenous customer demand, when customers internalize their expected cost of being bumped. We first consider the traditional setting in which compensation for bumped passengers is fixed and booking limits are the airline's only form of control. We provide sufficient conditions under which demand endogeneity leads to lower overbooking limits in this case. We then consider the broader problem of joint control of ticket price, bumping compensation, and booking limit. We show that price and bumping compensation can act as substitutes, which reduces the general problem to a more tractable one-dimensional search for optimal overbooking compensation and effectively allows the value of flying to be decoupled from the cost of being bumped. Finally, we extend our analysis to the case of auction-based compensation schemes and demonstrate that these generally outperform fixed compensation schemes. Numerical experiments that gauge magnitudes suggest that fixed-compensation policies that account for demand endogeneity can significantly outperform those that do not and that auction-based policies bring smaller but still significant additional gains.