Skip to main content
SpringerLink
Log in

The complexity of mean payoff games

  • Session 1A: Complexity Theory
  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

Included in the following conference series:

Abstract

We study the complexity of finding the values and optimal strategies of mean payoff games, a family of perfect information games introduced by Ehrenfeucht and Mycielski. We describe a pseudopolynomial time algorithm for the solution of such games, the decision problem for which is in NP ∩ co-NP. Finally, we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by Condon. These games are also known to be in NP ∩ co-NP, but no polynomial or pseudo-polynomial time algorithm is known for them.

Supported in part by the ESPRIT Basic Research Action Programme of the EC under contract No. 7141 (project ALCOM II).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Borodin, N. Linial, and M.E. Saks. An optimal on-line algorithm for metrical task system. Journal of the ACM, 39(4):745–763, 1992.

    Article  Google Scholar 

  2. R. Cole, R. Hariharan, M. Paterson, and U. Zwick. Tighter lower bounds on the exact complexity of string matching. SIAM Journal on Computing, 24:30–45, 1995.

    Article  Google Scholar 

  3. T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to algorithms. The MIT Press, 1990.

    Google Scholar 

  4. A. Condon. The complexity of stochastic games. Information and Computation, 96(2):203–224, February 1992.

    Article  Google Scholar 

  5. A. Ehrenfeucht and J. Mycielski. Positional strategies for mean payoff games. International Journal of Game Theory, 8:109–113, 1979.

    Article  Google Scholar 

  6. V.A. Gurvich, A.V. Karzanov, and L.G. Khachiyan. Cyclic games and an algorithm to find minimax cycle means in directed graphs. USSR Computational Mathematics and Mathematical Physics, 28:85–91, 1988.

    Article  Google Scholar 

  7. R.M. Karp. A characterization of the minimum cycle mean in a digraph. Discrete Mathematics, 23:309–311, 1978.

    Google Scholar 

  8. A.V. Karzanov and V.N. Lebedev. Cyclical games with prohibitions. Mathematical Programming, 60:277–293, 1993.

    Article  Google Scholar 

  9. W. Ludwig. A subexponential randomized algorithm for the simple stochastic game problem. Information and Computation, 117:151–155, 1995.

    Article  Google Scholar 

  10. V.R. Pratt. Every prime has a succinct certificate. SIAM Journal on Computing, 4(3):214–220, 1975.

    Article  Google Scholar 

  11. H.J.M. Peters and O.J. Vrieze. Surveys in game theory and related topics. CWI Tract 39, Centrum voor Wiskunde en Informatica, Amsterdam, 1987.

    Google Scholar 

  12. L.S. Shapley. Stochastic games. Proc. Nat. Acad. Sci. U.S.A., 39:1095–1100, 1953.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Uri Zwick

  2. Dept. of Computer Science, Univ. of Warwick, CV4 7AL, Coventry, UK

    Michael S. Paterson

Authors
  1. Uri Zwick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael S. Paterson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ding-Zhu Du Ming Li

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zwick, U., Paterson, M.S. (1995). The complexity of mean payoff games. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030814

Download citation

  • DOI: https://doi.org/10.1007/BFb0030814

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation