Journal of Applied Probability

Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information

Bernt Øksendal, Leif Sandal, and Jan Ubøe


We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer.

Article information

J. Appl. Probab., Volume 51A (2014), 213-226.

First available in Project Euclid: 2 December 2014

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Zentralblatt MATH identifier

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 91A15: Stochastic games

Vertical contracting stochastic differential game delayed information Itô-Lévy process


Øksendal, Bernt; Sandal, Leif; Ubøe, Jan. Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information. J. Appl. Probab. 51A (2014), 213--226. doi:10.1239/jap/1417528477.

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