Supplier Competition with Option Contracts for Discrete Blocks of Capacity

Abstract

When a firm faces an uncertain demand, it is common to procure supply using some type of option in addition to spot purchases. A typical version of this problem involves capacity being purchased in advance, with a separate payment made that applies only to the part of the capacity that is needed. We consider a discrete version of this problem in which competing suppliers choose a reservation price and an execution price for blocks of capacity, and the buyer, facing known distributions of demand and spot price, needs to decide which blocks to reserve. We show how to solve the buyer's (combinatorial) problem efficiently and also show that suppliers can do no better than offer blocks at execution prices that match their costs, making profits only from the reservation part of their bids. Finally we show that in an equilibrium the buyer selects the welfare maximizing set of blocks.

Keywords: supply options, competitive bidding, discrete blocks, submodularity, Nash equilibrium