  This paper studies a setting in which multiple suppliers compete for a
buyer's procurement business. The buyer faces uncertain demand and there is a
requirement to reserve capacity in advance of knowing the demand. Each supplier
has costs that are two dimensional, with some costs incurred before demand is
realized in order to reserve capacity and some costs incurred after demand is
realized at the time of delivery. A distinctive feature of our model is that
the marginal costs may not be constants, and this naturally leads us to a
supply function competition framework in which each supplier offers a schedule
of prices and quantities. We treat this problem as an example of a general
class of capacity games and show that, when the optimal supply chain profit is
submodular, in equilibrium the buyer makes a reservation choice that maximizes
the overall supply chain profit, each supplier makes a profit equal to their
marginal contribution to the supply chain, and the buyer takes the remaining
profit. We further prove that this submodularity property holds under two
commonly studied settings: (1) there are only two suppliers; and (2) in the
case of more than two suppliers, the marginal two-dimension costs of each
supplier are non-decreasing and constant, respectively.
