IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i12p1239-d297913.html
   My bibliography  Save this article

Moving Information Horizon Approach for Dynamic Game Models

Author

Listed:
  • Ovanes Petrosian

    (School of Automation, Qingdao University, Qingdao 266071, China)

  • Lihong Shi

    (Digital Workplace Product Technology Department, Huawei, Shenzhen 518000, China)

  • Yin Li

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskiy Prospekt, 35, Petergof, 198504 St. Petersburg, Russia)

  • Hongwei Gao

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

Abstract

In the paper, a new class of dynamic game models with a moving information horizon or dynamic updating is studied. In this class of games, players do not have full information about the game structure (motion equations, payoff functions) on the interval on which the game is defined. It is supposed that the players at each stage of the dynamic game have only truncated information about the game structure defined by the information horizon. Cooperative and noncooperative settings are considered in the paper. Results are illustrated using the oligopoly advertising game model, and comparison between the solution in the initial game model and in the game model with moving information horizon is presented. Simulation results are presented.

Suggested Citation

  • Ovanes Petrosian & Lihong Shi & Yin Li & Hongwei Gao, 2019. "Moving Information Horizon Approach for Dynamic Game Models," Mathematics, MDPI, vol. 7(12), pages 1-31, December.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1239-:d:297913
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/12/1239/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/7/12/1239/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Leon A. Petrosjan & Nikolay A. Zenkevich, 1996. "Differential games," World Scientific Book Chapters, in: Game Theory, chapter 5, pages 267-343, World Scientific Publishing Co. Pte. Ltd..
    2. Parkash Chander & Henry Tulkens, 2006. "A Core-Theoretic Solution for the Design of Cooperative Agreements on Transfrontier Pollution," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 176-193, Springer.
    3. D. W. K. Yeung & L. A. Petrosyan, 2011. "Subgame Consistent Cooperative Solution of Dynamic Games with Random Horizon," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 78-97, July.
    4. S. Jørgensen & G. Martín-Herrán & G. Zaccour, 2003. "Agreeability and Time Consistency in Linear-State Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 49-63, October.
    5. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    6. Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), 2006. "Public goods, environmental externalities and fiscal competition," Springer Books, Springer, number 978-0-387-25534-7, December.
    7. Jørgensen, Steffen & Zaccour, Georges, 2014. "A survey of game-theoretic models of cooperative advertising," European Journal of Operational Research, Elsevier, vol. 237(1), pages 1-14.
    8. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    9. David Yeung & Ovanes Petrosian, 2017. "Infinite Horizon Dynamic Games: A New Approach via Information Updating," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-23, December.
    10. Ovanes Petrosian & Andrey Barabanov, 2017. "Looking Forward Approach in Cooperative Differential Games with Uncertain Stochastic Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 328-347, January.
    Full references (including those not matched with items on IDEAS)

    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. Ovanes Petrosian, 2018. "About the Looking Forward Approach in Cooperative Differential Games with Transferable Utility," HSE Working papers WP BRP 183/EC/2018, National Research University Higher School of Economics.
    2. Pnevmatikos, Nikolaos & Vardar, Baris & Zaccour, Georges, 2018. "When should a retailer invest in brand advertising?," European Journal of Operational Research, Elsevier, vol. 267(2), pages 754-764.
    3. Chenavaz, Régis Y. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2020. "Modeling the impact of product quality on dynamic pricing and advertising policies," European Journal of Operational Research, Elsevier, vol. 284(3), pages 990-1001.
    4. Régis Chenavaz & Sajjad M. Jasimuddin, 2017. "An analytical model of the relationship between product quality and advertising," Post-Print hal-01685892, HAL.
    5. Salhab, Rabih & Le Ny, Jérôme & Malhamé, Roland P. & Zaccour, Georges, 2022. "Dynamic marketing policies with rating-sensitive consumers: A mean-field games approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1079-1093.
    6. Mariusz Górajski & Dominika Machowska, 2017. "Optimal double control problem for a PDE model of goodwill dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 425-452, June.
    7. Mukherjee, Arka & Carvalho, Margarida & Zaccour, Georges, 2023. "Managing quality and pricing during a product recall: An analysis of pre-crisis, crisis and post-crisis regimes," European Journal of Operational Research, Elsevier, vol. 307(1), pages 406-420.
    8. Zhou, Yong-Wu & Li, Jicai & Zhong, Yuanguang, 2018. "Cooperative advertising and ordering policies in a two-echelon supply chain with risk-averse agents," Omega, Elsevier, vol. 75(C), pages 97-117.
    9. Marc Artzrouni & Patrice Cassagnard, 2017. "Nerlove–Arrow: A New Solution to an Old Problem," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 267-280, January.
    10. Germain, Marc & Tulkens, Henry & Magnus, Alphonse, 2010. "Dynamic core-theoretic cooperation in a two-dimensional international environmental model," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 208-226, March.
    11. Luzon, Yossi & Pinchover, Rotem & Khmelnitsky, Eugene, 2022. "Dynamic budget allocation for social media advertising campaigns: optimization and learning," European Journal of Operational Research, Elsevier, vol. 299(1), pages 223-234.
    12. Yao, Fanjun & Parilina, Elena & Zaccour, Georges & Gao, Hongwei, 2022. "Accounting for consumers’ environmental concern in supply chain contracts," European Journal of Operational Research, Elsevier, vol. 301(3), pages 987-1006.
    13. Yohei Tenryu & Keita Kamei, 2014. "Dynamic Voluntary Advertising under Partial Market Coverage," KIER Working Papers 909, Kyoto University, Institute of Economic Research.
    14. Lambertini, Luca & Zaccour, Georges, 2015. "Inverted-U aggregate investment curves in a dynamic game of advertising," Economics Letters, Elsevier, vol. 132(C), pages 34-38.
    15. Marc GERMAIN & Henry TULKENS & Alphonse MAGNUS, 2009. "Dynamic core-theoretic cooperation in a two-dimensional international environmental model," LIDAM Discussion Papers IRES 2009015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    16. Tenryu, Yohei & Kamei, Keita, 2014. "Welfare Analysis of Dynamic Voluntary Advertising in Covered Markets," MPRA Paper 60694, University Library of Munich, Germany.
    17. Seidl, Andrea & Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2018. "Serious strategy for the makers of fun: Analyzing the option to switch from pay-to-play to free-to-play in a two-stage optimal control model with quadratic costs," European Journal of Operational Research, Elsevier, vol. 267(2), pages 700-715.
    18. Jørgensen, Steffen & Zaccour, Georges, 2019. "Optimal pricing and advertising policies for a one-time entertainment event," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 395-416.
    19. David Yeung & Ovanes Petrosian, 2017. "Infinite Horizon Dynamic Games: A New Approach via Information Updating," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-23, December.
    20. Jørgensen, Steffen & Zaccour, Georges, 2014. "A survey of game-theoretic models of cooperative advertising," European Journal of Operational Research, Elsevier, vol. 237(1), pages 1-14.

    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:gam:jmathe:v:7:y:2019:i:12:p:1239-:d:297913. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.