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Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game

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  • 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
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    References listed on IDEAS

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    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.
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