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Persistently Good Strategies for Nonleavable Stochastic Games with Finite State Space

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Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 6))

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Abstract

The notion of a persistently optimal strategy in gambling theory is analogous to that of subgame-perfect equilibria in game theory. We prove the existence of persistently E-optimal strategies for the players engaged in a nonleavable stochastic game with finite state space.

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References

  1. Blackwell, D. Positive dynamic programming, inProc. 5th Berkeley Symposium Math. Stat. Prob pp. 415–418, 1967.

    MathSciNet  Google Scholar 

  2. Dubins, L. E. and Sudderth, W. D. Persistently e-optimal strategiesMath. Oper. Res. pp. 125–134, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  3. Kumar, P. R. and Shiau, T. H. Existence of value and randomized strategies in zero-sum discrete time stochastic dynamic gamesSIAM J. Cont. Opt.617–634,1981.

    Article  MathSciNet  MATH  Google Scholar 

  4. Maitra, A. and Sudderth, W. D. An operator solution of stochastic gamesIsrael J. Math. pp. 33–49, 1992.

    Google Scholar 

  5. Maitra, A. and Sudderth, W. D.Discrete Gambling and Stochastic GamesSpringer-Verlag, New York, 1996.

    Book  MATH  Google Scholar 

  6. Nowak, A. S. Semicontinuous nonstationary stochastic gamesJ. Math. Anal. Appl. pp. 84–99, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  7. Secchi, P. Stationary strategies for recursive gamesMath. Oper. Res. 494–512, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  8. Secchi, P. On the existence of good stationary strategies for nonleavable stochastic gamesInt. J. Game Th. 61–81, 1998.

    Google Scholar 

  9. Selten, R. Spieltheoretische Behandlung eines Oligopolmodells mit NachfragetragheitZeitscrift fur die gesante Staatswissenschaft pp. 301–324, 1965.

    Google Scholar 

  10. van der Wal, J.Stochastic Dynamic Programming.The Mathematical Centre, Amsterdam 1981.

    MATH  Google Scholar 

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© 2001 Springer Science+Business Media New York

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Secchi, P., Sudderth, W.D. (2001). Persistently Good Strategies for Nonleavable Stochastic Games with Finite State Space. In: Altman, E., Pourtallier, O. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 6. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0155-7_8

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  • DOI: https://doi.org/10.1007/978-1-4612-0155-7_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6637-2

  • Online ISBN: 978-1-4612-0155-7

  • eBook Packages: Springer Book Archive

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