Scandinavian Working Papers in Economics

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

No 2012/2: Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand

Leif K. Sandal () and Jan Ubøe ()
Additional contact information
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 consider Stackelberg games in a multiperiod vertical contracting model with uncertain demand. Demand has a distribution with a mean and variance that depend on the current retail price, and this dependence may vary from period to period. We focus on a class of problems in which the market has a memory-based scaling of demand, and the mean scaling is a function of previous retail prices. This leads to a strategic game in which the parties must balance high immediate profits with reduced future earnings. We propose a complete solution to this multiperiod Stackelberg game, covering cases with finite and infinite horizons. The theory is illustrated by using a Cobb-Douglas demand function with an additive, normally distributed random term, but the theory applies to more general settings.

Keywords: Stackelberg game; multiperiod vertical contracting model; price-dependent demand

JEL-codes: C61; C73; D81

27 pages, February 27, 2012

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