IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v7y2017i4d10.1007_s13235-016-0211-5.html
   My bibliography  Save this article

Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game

Author

Listed:
  • Dipti Dubey

    (Indian Statistical Institute)

  • S. K. Neogy

    (Indian Statistical Institute)

  • Debasish Ghorui

    (Jadavpur University)

Abstract

In this paper, we revisit a result by Jurg et al. (Linear Algebra Appl 141:61–74, 1990) where the necessary and sufficient condition for a bimatrix game to be weakly completely mixed is given. We present an alternate proof of this result using linear complementarity approach. We extend this result to a generalization of bimatrix game introduced by Gowda and Sznajder (Int J Game Theory 25:1–12, 1996) via a generalization of linear complementarity problem introduced by Cottle and Dantzig (J Comb Theory 8:79–90, 1970). We further study completely mixed switching controller stochastic game (in which transition structure is a natural generalization of the single controller games) and extend the results obtained by Filar (Proc Am Math Soc 95:585–594, 1985) for completely mixed single controller stochastic game to completely mixed switching controller stochastic game. A numerical method is proposed to compute a completely mixed strategy for a switching controller stochastic game.

Suggested Citation

  • Dipti Dubey & S. K. Neogy & Debasish Ghorui, 2017. "Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 535-554, December.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0211-5
    DOI: 10.1007/s13235-016-0211-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-016-0211-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-016-0211-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jurg, A.P. & Jansen, M.J.M. & Parthasarathy, T. & Tijs, S.H., 1990. "On weakly completely mixed bimatrix games," Other publications TiSEM 0d242326-fe51-40af-be8f-d, Tilburg University, School of Economics and Management.
    2. S. R. Mohan & S. K. Neogy & T. Parthasarathy, 2001. "Pivoting Algorithms For Some Classes Of Stochastic Games: A Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 253-281.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. Vrieze, O.J. & Tijs, S.H. & Raghavan, T.E.S. & Filar, J.A., 1983. "A finite algorithm for the switching control stochastic game," Other publications TiSEM 61df4c61-65ea-4357-99c0-1, Tilburg University, School of Economics and Management.
    5. Gowda, M Seetharama & Sznajder, Roman, 1996. "A Generalization of the Nash Equilibrium Theorem on Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 1-12.
    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. Prasenjit Mondal, 2018. "Completely mixed strategies for single controller unichain semi-Markov games with undiscounted payoffs," Operational Research, Springer, vol. 18(2), pages 451-468, July.
    2. K. C. Sivakumar & M. S. Gowda & G. Ravindran & Usha Mohan, 2020. "Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India," Annals of Operations Research, Springer, vol. 287(2), pages 565-572, April.
    3. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    4. S. K. Neogy & Prasenjit Mondal & Abhijit Gupta & Debasish Ghorui, 2018. "On Solving Mean Payoff Games Using Pivoting Algorithms," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-26, October.
    5. N. Krishnamurthy & S. K. Neogy, 2020. "On Lemke processibility of LCP formulations for solving discounted switching control stochastic games," Annals of Operations Research, Springer, vol. 295(2), pages 633-644, December.
    6. Karan N. Chadha & Ankur A. Kulkarni, 2022. "On independent cliques and linear complementarity problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1036-1057, December.
    7. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Discussion Paper 2005-5, Tilburg University, Center for Economic Research.
    8. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    9. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    10. Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    11. Guo-qiang Wang & Yu-jing Yue & Xin-zhong Cai, 2009. "Weighted-path-following interior-point algorithm to monotone mixed linear complementarity problem," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 435-445, December.
    12. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2011. "Solving discrete systems of nonlinear equations," Other publications TiSEM 81f0a46c-3c9d-4757-bfa1-0, Tilburg University, School of Economics and Management.
    13. E. Demidenko, 2008. "Criteria for Unconstrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 375-395, March.
    14. R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    15. Zheng, Hua & Vong, Seakweng & Liu, Ling, 2019. "A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 396-405.
    16. Zheng-Hai Huang & Yu-Fan Li & Yong Wang, 2023. "A fixed point iterative method for tensor complementarity problems with the implicit Z-tensors," Journal of Global Optimization, Springer, vol. 86(2), pages 495-520, June.
    17. G. Isac & S. Z. Németh, 2008. "REFE-Acceptable Mappings: Necessary and Sufficient Condition for the Nonexistence of a Regular Exceptional Family of Elements," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 507-520, June.
    18. Christoph Böhringer & Thomas F. Rutherford, 2017. "Paris after Trump: An Inconvenient Insight," CESifo Working Paper Series 6531, CESifo.
    19. Songfeng Zheng, 2021. "KLERC: kernel Lagrangian expectile regression calculator," Computational Statistics, Springer, vol. 36(1), pages 283-311, March.
    20. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.

    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:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0211-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.