Deterministic Priority Mean-Payoff Games as Limits of Discounted Games

  • Hugo Gimbert
  • Wiesław Zielonka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)


Inspired by the paper of de Alfaro, Henzinger and Majumdar [1] about discounted μ-calculus we show new surprising links between parity games and different classes of discounted games.


Utility Mapping Discount Factor Markov Decision Process Stochastic Game Discount Mapping 
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  1. 1.
    de Alfaro, L., Henzinger, T.A., Majumdar, R.: Discounting the future in systems theory. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1022–1037. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Mertens, J.F., Neyman, A.: Stochastic games. International Journal of Game Theory 10, 53–56 (1981)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Emerson, E.A., Jutla, C.: Tree automata, μ-calculus and determinacy. In: FOCS 1991, pp. 368–377. IEEE Computer Society Press, Los Alamitos (1991)Google Scholar
  4. 4.
    Shapley, L.S.: Stochastic games. Proceedings Nat. Acad. of Science USA 39, 1095–1100 (1953)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gimbert, H., Zielonka, W.: Games where you can play optimally without any memory. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 428–442. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Hordijk, A., Yushkevich, A.: Blackwell optimality. In: Feinberg, E., Schwartz, A. (eds.) Handbook of Markov Decision Processes, Kluwer, Dordrecht (2002)Google Scholar
  7. 7.
    Blackwell, D.: Discrete dynamic programming. Annals of Mathematical Statistics 33, 719–726 (1962)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Raghavan, T.E.S., Syed, Z.: A policy-improvement type algorithm for solving zero-sum two-person stochastic games of perfect information. Math. Program. 95(3), 513–532 (2003)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Vöge, J., Jurdziński, M.: A discrete strategy improvement algorithm for solving parity games. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 202–215. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Jurdziński, M.: Deciding the winner in parity games is in UP ∩ co-UP. Information Processing Letters 68(3), 119–124 (1998)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Zwick, U., Paterson, M.: The complexity of mean payoff games on graphs. Theor. Computer Science 158(1-2), 343–359 (1996)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hugo Gimbert
    • 1
  • Wiesław Zielonka
    • 2
  1. 1.Instytut InformatykiWarsaw UniversityPoland
  2. 2.Université Paris 7 and CNRS, LIAFA, case 7014ParisFrance

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