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Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand

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Author Info

  • Sandal, Leif K.

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Ubøe, Jan

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

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.

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Bibliographic Info

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2012/2.

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Length: 27 pages
Date of creation: 27 Feb 2012
Date of revision:
Handle: RePEc:hhs:nhhfms:2012_002

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Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
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Fax: +47 55 95 96 50
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Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Related research

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

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References

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  1. Xu, Minghui & Chen, Youhua (Frank) & Xu, Xiaolin, 2010. "The effect of demand uncertainty in a price-setting newsvendor model," European Journal of Operational Research, Elsevier, vol. 207(2), pages 946-957, December.
  2. Øksendal, Bernt & Sandal, Leif K. & Ubøe, Jan, 2011. "Stochastic Stackelberg equilibria with applications to time dependent newsvendor models," Discussion Papers 2011/9, Department of Business and Management Science, Norwegian School of Economics.
  3. Qin, Yan & Wang, Ruoxuan & Vakharia, Asoo J. & Chen, Yuwen & Seref, Michelle M.H., 2011. "The newsvendor problem: Review and directions for future research," European Journal of Operational Research, Elsevier, vol. 213(2), pages 361-374, September.
  4. Martin A. Lariviere & Evan L. Porteus, 2001. "Selling to the Newsvendor: An Analysis of Price-Only Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 293-305, May.
  5. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
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Cited by:
  1. Andersson, Jonas & Jörnsten, Kurt & Nonås, Sigrid Lise & Sandal, Leif K. & Ubøe, Jan, 2011. "A maximum entropy approach to the newsvendor problem with partial information," Discussion Papers 2011/14, Department of Business and Management Science, Norwegian School of Economics.

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