Advertisement

Nash Equilibria for Reachability Objectives in Multi-player Timed Games

  • Patricia Bouyer
  • Romain Brenguier
  • Nicolas Markey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6269)

Abstract

We propose a procedure for computing Nash equilibria in multi-player timed games with reachability objectives. Our procedure is based on the construction of a finite concurrent game, and on a generic characterization of Nash equilibria in (possibly infinite) concurrent games. Along the way, we use our characterization to compute Nash equilibria in finite concurrent games.

Keywords

Nash Equilibrium Transition System Stochastic Game Winning Strategy Time Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alur, R., Dill, D.L.: A theory of timed automata. TCS 126(2), 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49, 672–713 (2002)MathSciNetGoogle Scholar
  3. 3.
    Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: Proc. IFAC Symp. System Structure and Control, pp. 469–474. Elsevier, Amsterdam (1998)Google Scholar
  4. 4.
    Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: UPPAAL-Tiga: Time for playing games! In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Bouyer, P., Brenguier, R., Markey, N.: Nash equilibria for reachability objectives in multi-player timed games. Research report LSV-10-12, Lab. Spécification & Vérification, ENS Cachan, France (June 2010)Google Scholar
  6. 6.
    Chatterjee, K., Henzinger, T.A., Jurdziński, M.: Games with secure equilibria. In: LICS 2006, pp. 160–169. IEEE Comp. Soc. Press, Los Alamitos (2006)Google Scholar
  7. 7.
    Chatterjee, K., Majumdar, R., Jurdziński, M.: On Nash equilibria in stochastic games. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 26–40. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: The element of surprise in timed games. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 142–156. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Félegyházi, M., Hubaux, J.-P., Buttyán, L.: Nash equilibria of packet forwarding strategies in wireless ad hoc networks. IEEE Trans. Mobile Computing 5(5), 463–476 (2006)CrossRefGoogle Scholar
  10. 10.
    Henzinger, T.A.: Games in system design and verification. In: TARK 2005, pp. 1–4. Nat. Univ., Singapore (2005)Google Scholar
  11. 11.
    Jurdziński, M., Laroussinie, F., Sproston, J.: Model checking probabilistic timed automata with one or two clocks. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 170–184. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Laroussinie, F., Markey, N., Oreiby, G.: On the expressiveness and complexity of ATL. LMCS 4(2:7) (2008)Google Scholar
  13. 13.
    Nash, J.F.: Equilibrium points in n-person games. Proc. National Academy of Sciences of the USA 36(1), 48–49 (1950)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Paul, S., Simon, S.: Nash equilibrium in generalised Muller games. In: FSTTCS 2009. LIPIcs, vol. 4, pp. 335–346. LZI (2009)Google Scholar
  15. 15.
    Thomas, W.: Infinite games and verification (extended abstract of a tutoral). In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 58–64. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Ummels, M.: Rational behaviour and strategy construction in infinite multiplayer games. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 212–223. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Ummels, M.: The complexity of Nash equilibria in infinite multiplayer games. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 20–34. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Ummels, M., Wojtczak, D.: The complexity of Nash equilibria in simple stochastic multiplayer games. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 297–308. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Ummels, M., Wojtczak, D.: Decision problems for Nash equilibria in stochastic games. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 515–530. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Walukiewicz, I.: Pushdown processes: Games and model checking. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 234–263. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Romain Brenguier
    • 1
  • Nicolas Markey
    • 1
  1. 1.LSV, ENS Cachan & CNRSFrance

Personalised recommendations