Stackelberg Equilibria in a Multiperiod Vertical Contracting Model with Uncertain and Price-Dependent Demand

28 Pages Posted: 16 Mar 2012

See all articles by Leif Kristoffer Sandal

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science

Jan Uboe

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: February 27, 2012

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 Classification: C61, C73, D81

Suggested Citation

Sandal, Leif Kristoffer and Uboe, Jan, Stackelberg Equilibria in a Multiperiod Vertical Contracting Model with Uncertain and Price-Dependent Demand (February 27, 2012). NHH Dept. of Finance & Management Science Discussion Paper No. 2012/2, Available at SSRN: https://ssrn.com/abstract=2024927 or http://dx.doi.org/10.2139/ssrn.2024927

Leif Kristoffer Sandal

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway
+47 55 95 93 41 (Phone)

Jan Uboe (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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