IDEAS home Printed from https://ideas.repec.org/p/hhs/nhhfms/2012_002.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • Sandal, Leif K. & Ubøe, Jan, 2012. "Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand," Discussion Papers 2012/2, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2012_002
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/11250/164188
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Øksendal, Bernt & Sandal, Leif & Ubøe, Jan, 2013. "Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1284-1299.
    2. 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.
    3. 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.
    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. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    6. Edwin S. Mills, 1959. "Uncertainty and Price Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 73(1), pages 116-130.
    7. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Øksendal, Bernt & Sandal, Leif & Ubøe, Jan, 2013. "Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1284-1299.
    2. Weiwei Zhang & Zhongfei Li & Ke Fu & Fan Wang, 2017. "Effect of the Return Policy in a Continuous-Time Newsvendor Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-28, December.
    3. Andersson, Jonas & Jörnsten, Kurt & Nonås, Sigrid Lise & Sandal, Leif & Ubøe, Jan, 2013. "A maximum entropy approach to the newsvendor problem with partial information," European Journal of Operational Research, Elsevier, vol. 228(1), pages 190-200.
    4. Azad Gholami, Reza & Sandal, Leif K. & Ubøe, Jan, 2016. "Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand," Discussion Papers 2016/6, Norwegian School of Economics, Department of Business and Management Science.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Azad Gholami, Reza & Sandal, Leif K. & Ubøe, Jan, 2016. "Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand," Discussion Papers 2016/6, Norwegian School of Economics, Department of Business and Management Science.
    2. Gholami, Reza Azad & Sandal, Leif Kristoffer & Ubøe, Jan, 2021. "A solution algorithm for multi-period bi-level channel optimization with dynamic price-dependent stochastic demand," Omega, Elsevier, vol. 102(C).
    3. Serel, Doğan A., 2015. "Production and pricing policies in dual sourcing supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 76(C), pages 1-12.
    4. Serel, Doğan A., 2017. "A single-period stocking and pricing problem involving stochastic emergency supply," International Journal of Production Economics, Elsevier, vol. 185(C), pages 180-195.
    5. Rubio-Herrero, Javier & Baykal-Gürsoy, Melike, 2020. "Mean-variance analysis of the newsvendor problem with price-dependent, isoelastic demand," European Journal of Operational Research, Elsevier, vol. 283(3), pages 942-953.
    6. Yong Liu & Michael J. Fry & Amitabh S. Raturi, 2006. "Vertically restrictive pricing in supply chains with price‐dependent demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 485-501, September.
    7. Brito, Anderson J. & de Almeida, Adiel T., 2012. "Modeling a multi-attribute utility newsvendor with partial backlogging," European Journal of Operational Research, Elsevier, vol. 220(3), pages 820-830.
    8. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    9. Kyparisis, George J. & Koulamas, Christos, 2018. "The price-setting newsvendor problem with nonnegative linear additive demand," European Journal of Operational Research, Elsevier, vol. 269(2), pages 695-698.
    10. Lee, Eunji & Minner, Stefan, 2024. "How power structure and markup schemes impact supply chain channel efficiency under price-dependent stochastic demand," European Journal of Operational Research, Elsevier, vol. 318(1), pages 297-309.
    11. Stefanos Leonardos & Costis Melolidakis & Constandina Koki, 2022. "Monopoly pricing in vertical markets with demand uncertainty," Annals of Operations Research, Springer, vol. 315(2), pages 1291-1318, August.
    12. Mitra, Subrata, 2018. "Newsvendor problem with clearance pricing," European Journal of Operational Research, Elsevier, vol. 268(1), pages 193-202.
    13. Bai, Tian & Wu, Meng & Zhu, Stuart X., 2019. "Pricing and ordering by a loss averse newsvendor with reference dependence," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 343-365.
    14. Kyparisis, George J. & Koulamas, Christos, 2018. "Optimal pricing and seat allocation for a two-cabin airline revenue management problem," International Journal of Production Economics, Elsevier, vol. 201(C), pages 18-25.
    15. Kuo-Hsien Wang & Yu-Je Lee & Che-Tsung Tung, 2013. "Optimal Prices and Inventories Decisions on Returns Policy with Practical Examples Thorough a Stackelberg Game," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 3(2), pages 66-77, April.
    16. Azad Gholami, Reza & Sandal, Leif K. & Ubøe, Jan, 2019. "Markets With Memory: Dynamic Channel Optimization Models With Price-Dependent Stochastic Demand," Discussion Papers 2019/8, Norwegian School of Economics, Department of Business and Management Science.
    17. Abad, Prakash, 2014. "Determining optimal price and order size for a price setting newsvendor under cycle service level," International Journal of Production Economics, Elsevier, vol. 158(C), pages 106-113.
    18. Liu, Yong & Fry, Michael J. & Raturi, Amitabh S., 2009. "Retail price markup commitment in decentralized supply chains," European Journal of Operational Research, Elsevier, vol. 192(1), pages 277-292, January.
    19. Schulte, Benedikt & Sachs, Anna-Lena, 2020. "The price-setting newsvendor with Poisson demand," European Journal of Operational Research, Elsevier, vol. 283(1), pages 125-137.
    20. Jiri Chod & Nils Rudi, 2005. "Resource Flexibility with Responsive Pricing," Operations Research, INFORMS, vol. 53(3), pages 532-548, June.

    More about this item

    Keywords

    Stackelberg game; multiperiod vertical contracting model; price-dependent demand;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:nhhfms:2012_002. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Stein Fossen (email available below). General contact details of provider: https://edirc.repec.org/data/dfnhhno.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.