Advance booking discount programs under retail competition

We model a situation in which two retailers consider launching an "Advance Booking Discount" (ABD) program. In this program, customers are enticed to precommit their orders at a discount price prior to the regular selling season. However, these precommitted orders are filled during the selling season. While the ABD program enables the retailers to lock in a portion of the customer demand and use this demand information to develop more accurate forecasts and supply plans, the ABD price reduces profit margin. We analyze the four possible scenarios wherein each of the two firms offer an ABD program or not, and establish conditions under which the unique equilibrium calls for launching the ABD program at both retailers.