Abstract
We consider infinite antagonistic games over finite graphs. We present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies. To verify the robustness of our conditions we show that all popular payoff mappings, such as mean payoff, discounted, parity as well as several other payoffs satisfy them.
This research was supported by European Research Training Network: Games and Automata for Synthesis and Validation
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Björklund, H., Sandberg, S., Vorobyov, S.: Memoryless determinacy of parity and mean payoff games: a simple proof. Theor. Computer Science 310, 365–378 (2004)
de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Model checking discounted temporal properties. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 77–92. Springer, Heidelberg (2004)
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)
Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. Intern. J. of Game Theory 8, 109–113 (1979)
Emerson, E.A., Jutla, C.: Tree automata, μ-calculus and determinacy. In: FOCS 1991, pp. 368–377. IEEE Computer Society Press, Los Alamitos (1991)
Filar, J., Vrieze, K.: Competitive Markov Decision Processes. Springer, Heidelberg (1997)
Gurevich, Y., Harrington, L.: Trees, automata and games. In: Proc. 17th Symp. on the Theory of Comp., pp. 60–65. IEEE Computer Society Press, Los Alamitos (1982)
Maitra, A.P., Sudderth, W.D.: Discrete Gambling and Stochastic Games. Springer, Heidelberg
Mostowski, A.W.: Games with forbidden positions. Technical Report 78, Uniwersytet Gdański, Instytut Matematyki (1991)
Moulin, H.: Prolongements des jeux á deux joueurs de somme nulle. Une théorie abstraite des duels. Bull. Soc. math. France, pp. 1–111 (1976), Mémoire 45
Raghavan, T.E.S.: Finite-step algorithms for single-controller and perfect information stochastic games. In: Neyman, A., Sorin, S. (eds.) Stohastic Games and Applications. NATO Science Series C, Mathematical and Physical Sciences, vol. 570, pp. 227–251. Kluwer Academic Publishers, Dordrecht (2003)
Shapley, L.S.: Stochastic games. Proceedings Nat. Acad. of Science USA 39, 1095–1100 (1953)
Zielonka, W.: Perfect-information stochastic parity games. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 499–513. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gimbert, H., Zielonka, W. (2004). When Can You Play Positionally?. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_53
Download citation
DOI: https://doi.org/10.1007/978-3-540-28629-5_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22823-3
Online ISBN: 978-3-540-28629-5
eBook Packages: Springer Book Archive