Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2011/9: Stochastic Stackelberg equilibria with applications to time dependent newsvendor models

Bernt Øksendal (), Leif K. Sandal () and Jan Ubøe ()
Additional contact information
Bernt Øksendal: Dept. of Mathematics, University of Oslo, Postal: University of Oslo, Department of Mathematics, Postboks 1053 Blindern, 0316 Oslo, Norway
Leif K. Sandal: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Jan Ubøe: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: In this paper we prove a sufficient maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits under a random demand rate. Our demand rate is an Ito-Levy process, and to increase realism information is delayed, e.g., due to production time. 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, these results are operational because we are able to offer explicit solution formulas. An interesting finding is that more precise information may be a considerable disadvantage for the retailer.

Keywords: Stochastic differential games; newsvendor model; delayed information; Ito-Levy processes

JEL-codes: C00

37 pages, May 19, 2011

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