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

Capacity Games with Supply Function Competition