Strategic advance sales, demand uncertainty and overcommitment

We study a game in which producers can sell both before and after the realization of a random demand. Models of strategic forward trading and of advance sales to intermediaries or consumers share this structure. Demand uncertainty and committed advance sales imply that final-stage net residual demand may be so low that producers find additional sales unprofitable, or even so low that the final period price is zero, introducing some convexity into producers’ payoffs. If such an ex-post overcommitment occurs on the equilibrium path, producers reduce their advance sales, muting the pro-competitive effects found under deterministic demand. We prove existence of a unique symmetric pure-strategy equilibrium, whose nature depends on the support of the demand distribution relative to the marginal cost of production. For a narrow support, existence is assured for any distribution, while for wider support we establish a sufficient condition for existence. Our results provide a precise characterization of “minor” uncertainty, in which only the expected value of demand affects the equilibrium which is otherwise qualitatively similar to the deterministic case.