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

Part of: Game theory Stochastic analysis

Published online by Cambridge University Press:  30 March 2016

Bernt Øksendal ,
Leif Sandal  and
Jan Ubøe
Bernt Øksendal
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway
Leif Sandal
Affiliation:
Norwegian School of Economics, Helleveien 30, 5045 Bergen, Norway
Jan Ubøe
Affiliation:
Norwegian School of Economics, Helleveien 30, 5045 Bergen, Norway. Email address: [email protected].
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Abstract

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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.

Keywords

Vertical contractingstochastic differential gamedelayed informationItô-Lévy process

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 91A15: Stochastic games
Type
Part 5. Finance and econometrics
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 213 - 226
Copyright
Copyright © Applied Probability Trust 2014 

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