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Zero-Sum Stochastic Games with Partial Information and Average Payoff

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Abstract

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.

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References

  1. Shapley, L.: Stochastic games. Proc. Natl. Acad. Sci. 39, 1095–1100 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  2. Vrieze, K.: Zero-sum stochastic games: a survey. Quart. - Cent. Wiskd. Inform. 2, 147–170 (1989)

    MATH  MathSciNet  Google Scholar 

  3. Borkar, V.S.: Dynamic programming for ergodic control with partial observations. Stoch. Process. Appl. 103, 293–310 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bertsekas, D.P., Shreve, S.E.: Stochastic Optimal Control. Academic Press, New York (1978)

    MATH  Google Scholar 

  5. Dynkin, E.B., Yushkevich, A.: Controlled Markov Processes. Springer, Berlin (1979)

    Book  Google Scholar 

  6. Ghosh, M.K., McDonald, D., Sinha, S.: Zero-sum stochastic games with partial information. J. Optim. Theory Appl. 121, 99–118 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Athreya, K.B., Ney, P.: A new approach to the limit theory of recurrent Markov chains. Trans. Am. Math. Soc. 245, 493–501 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  8. Nummelin, E.: A splitting technique for Harris recurrent chains. Z. Wahrscheinlichkeitstheor. Verw. Geb. 43, 309–318 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  9. Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Springer, London (1993)

    Book  MATH  Google Scholar 

  10. Arapostathis, A., Borkar, V.S., Ghosh, M.K.: Ergodic Control of Diffusion Processes. Cambridge University Press, Cambridge (2011)

    Book  Google Scholar 

  11. Hernández-Lerma, O., Lasserre, J.B.: Further Topics on Discrete-Time Markov Control Processes. Springer, New York (1999)

    Book  MATH  Google Scholar 

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Acknowledgements

The author wish to thank V.S. Borkar and M.K. Ghosh for many helpful discussions and comments.

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Correspondence to Subhamay Saha.

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This work is supported in part by SPM fellowship of CSIR and in part by UGC Centre for Advanced Study.

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Saha, S. Zero-Sum Stochastic Games with Partial Information and Average Payoff. J Optim Theory Appl 160, 344–354 (2014). https://doi.org/10.1007/s10957-013-0359-8

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  • DOI: https://doi.org/10.1007/s10957-013-0359-8

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