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Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game

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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.

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Acknowledgements

The authors would like to thank the anonymous referees for their constructive suggestions which considerably improve the overall presentation of the paper. The first author wants to thank the National Board of Higher Mathematics (NBHM), India, for financial support for this research.

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Authors and Affiliations

  1. Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi, 110016, India

    Dipti Dubey & S. K. Neogy

  2. Jadavpur University, Kolkata, 700032, India

    Debasish Ghorui

Authors
  1. Dipti Dubey
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  2. S. K. Neogy
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  3. Debasish Ghorui
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Correspondence to S. K. Neogy.

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Dubey, D., Neogy, S.K. & Ghorui, D. Completely Mixed Strategies for Generalized Bimatrix and Switching Controller Stochastic Game. Dyn Games Appl 7, 535–554 (2017). https://doi.org/10.1007/s13235-016-0211-5

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