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Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models

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  • Øksendal, Bernt
  • Sandal, Leif
  • Ubøe, Jan

Abstract

In this paper, we prove a 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 Itô–Lévy process, and to increase realism information is delayed, e.g., due to production time. A special feature of our time-continuous model is that it allows for a price-dependent demand, thereby opening for strategies where pricing is used to manipulate the demand.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:7:p:1284-1299
    DOI: 10.1016/j.jedc.2013.02.010
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    Cited by:

    1. 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).
    2. Reza Azad Gholami & Leif Kristoffer Sandal & Jan Ubøe, 2022. "Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts," Games, MDPI, vol. 13(6), pages 1-26, October.
    3. 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.
    4. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    5. Albrecht, E & Baum, Günter & Birsa, R & Bradamante, F & Bressan, A & Chapiro, A & Cicuttin, A & Ciliberti, P & Colavita, A & Costa, S & Crespo, M & Cristaudo, P & Dalla Torre, S & Diaz, V & Duic, V &, 2010. "Results from COMPASS RICH-1," Center for Mathematical Economics Working Papers 535, Center for Mathematical Economics, Bielefeld University.
    6. Azad Gholami, Reza & Sandal, Leif Kristoffer & Ubøe, Jan, 2024. "Who benefits from postponement in multi-period supply channel optimization?," Omega, Elsevier, vol. 123(C).
    7. 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.
    8. Li Chen & Peipei Zhou & Hua Xiao, 2023. "Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    9. Kogan, Konstantin & Chernonog, Tatyana, 2019. "Competition under industry-stock-driven prevailing market price: Environmental consequences and the effect of uncertainty," European Journal of Operational Research, Elsevier, vol. 276(3), pages 929-946.
    10. 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.
    11. 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.
    12. Jingtang Ma & Shan Yang, 2024. "High-dimensional stochastic control models for newsvendor problems and deep learning resolution," Annals of Operations Research, Springer, vol. 339(1), pages 789-811, August.
    13. Youkyung Won, 2016. "Dominance Relationship Among the Retailer’s Strategies Under the Semi-Stackelberg Newsvendor Situation with Quantity Discounts," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(02), pages 1-20, April.
    14. Zheng, Yueyang & Shi, Jingtao, 2022. "A linear-quadratic partially observed Stackelberg stochastic differential game with application," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    15. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
    16. Ata Allah Taleizadeh & Mahsa Noori-daryan & Kannan Govindan, 2016. "Pricing and ordering decisions of two competing supply chains with different composite policies: a Stackelberg game-theoretic approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2807-2836, May.
    17. Alavi Fard, Farzad & He, Jian & Ivanov, Dmitry & Jie, Ferry, 2019. "A utility adjusted newsvendor model with stochastic demand," International Journal of Production Economics, Elsevier, vol. 211(C), pages 154-165.
    18. Wang, Yu & Yan, Zhiguo, 2023. "Pareto-based Stackelberg differential game for stochastic systems with multi-followers," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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    More about this item

    Keywords

    Stochastic differential games; Delayed information; Itô–Lévy processes; Stackelberg equilibria; Newsvendor models; Optimal control of forward-backward stochastic differential equations;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • 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

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