Online Addendum for “Dynamic Procurement, Quantity Discounts, and Supply Chain Efficiency”

In this section, we consider the case where the supplier has a capacity of K units that he can sell throughout N -periods. Let QN correspond to the total production quantity of an N -period uncapacitated game. For the N -period limited capacity case, when the capacity is “tight,” i.e., CS ≤ a 4b , or when the capacity is “abundant,” i.e., CS ≥ QN , the results are straightforward and intuitive. In the first case, as the capacity is tight, the supplier does not change his price through the game, so the N -period game is equivalent to a single period game. When CS ≥ QN , the problem is equivalent to an unlimited capacity game (Proposition 1). What happens in between these extremes is more interesting. Our main result is as follows.