Advertisement

Journal of Optimization Theory and Applications

, Volume 160, Issue 1, pp 344–354 | Cite as

Zero-Sum Stochastic Games with Partial Information and Average Payoff

  • Subhamay SahaEmail author
Article

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.

Keywords

Stochastic games Partial observation Average payoff Saddle point strategies 

Notes

Acknowledgements

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

References

  1. 1.
    Shapley, L.: Stochastic games. Proc. Natl. Acad. Sci. 39, 1095–1100 (1953) CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Vrieze, K.: Zero-sum stochastic games: a survey. Quart. - Cent. Wiskd. Inform. 2, 147–170 (1989) zbMATHMathSciNetGoogle Scholar
  3. 3.
    Borkar, V.S.: Dynamic programming for ergodic control with partial observations. Stoch. Process. Appl. 103, 293–310 (2003) CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bertsekas, D.P., Shreve, S.E.: Stochastic Optimal Control. Academic Press, New York (1978) zbMATHGoogle Scholar
  5. 5.
    Dynkin, E.B., Yushkevich, A.: Controlled Markov Processes. Springer, Berlin (1979) CrossRefGoogle Scholar
  6. 6.
    Ghosh, M.K., McDonald, D., Sinha, S.: Zero-sum stochastic games with partial information. J. Optim. Theory Appl. 121, 99–118 (2004) CrossRefzbMATHMathSciNetGoogle Scholar
  7. 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) CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Nummelin, E.: A splitting technique for Harris recurrent chains. Z. Wahrscheinlichkeitstheor. Verw. Geb. 43, 309–318 (1978) CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Meyn, S.P., Tweedie, R.L.: Markov Chains and Stochastic Stability. Springer, London (1993) CrossRefzbMATHGoogle Scholar
  10. 10.
    Arapostathis, A., Borkar, V.S., Ghosh, M.K.: Ergodic Control of Diffusion Processes. Cambridge University Press, Cambridge (2011) CrossRefGoogle Scholar
  11. 11.
    Hernández-Lerma, O., Lasserre, J.B.: Further Topics on Discrete-Time Markov Control Processes. Springer, New York (1999) CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations