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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
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    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, October.
    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.
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