Abstract
When seeking to coordinate in a game with imperfect information, it is often relevant for a player to know what other players know. Keeping track of the information acquired in a play of infinite duration may, however, lead to infinite hierarchies of higher-order knowledge. We present a construction that makes explicit which higher-order knowledge is relevant in a game and allows us to describe a class of games that admit coordinated winning strategies with finite memory.
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References
Arnold, A., & Walukiewicz, I. (2007). Nondeterministic controllers of nondeterministic processes. In Logic and automata (Vol. 2). Amsterdam University Press.
Berwanger, D. (2010). Infinite coordination games. In Logic and the foundations of game and decision theory (LOFT9), texts in logic and games. Amsterdam University Press, To appear.
Chandra A. K., Kozen D., Stockmeyer L. J. (1981) Alternation. Journal of ACM 28: 114–133
Chatterjee, K., Doyen, L., Henzinger, T. A., & Raskin, J.-F. (2006). Algorithms for omega-regular games with imperfect information. In Proceedings of the 20th International Workshop on Computer Science Logic (CSL), 15th Annual Conference of the EACSL, Vol. 4207 of LNCS (pp. 287–302). Springer.
Gale D., Stewart F. M. (1953) Infinite games with perfect information. Annals of Mathematics Studies 28: 245–266
Gastin P., Sznajder N., Zeitoun M. (2009) Distributed synthesis for well-connected architectures. Formal Methods in System Design 34: 215–237
Henzinger, T. A. (2005) Games in system design and verification. In Proceedings of the 10th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-2005).
Kupferman, O., & Vardi, M. Y. (2001). Synthesizing distributed systems, In Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science.
McNaughton R. (1993) Infinite games played on finite graphs. Annals of Pure and Applied Logic 65: 149–184
Peterson, G. L., & Reif, J. H. (1979). Multiple-Person alternation. In Proceedings of the 20th Annual Symposium on Foundations of Computer Science, (FOCS 1979), IEEE (pp. 348–363).
Pnueli, A., & Rosner, E. (1989). On the synthesis of a reactive module. In Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (pp. 179–190). ACM Press.
Ramadge P. J., Wonham W. M. (1987) Supervisory control of a class of discrete event processes. SIAM Journal Control and Optimization 25: 206–230
Reif J. (1984) The complexity of two-player games of incomplete information. Journal of Computer and System Sciences 29: 274–301
Rudie, K., & Wonham, W. M. (1990). Supervisory control of communicating processes. In L. Logrippo, R. L. Probert, & H. Ural (Eds.), Proceedings of PSTV 1990, Tenth International Symposium on Protocol Specification, Testing and Verification (pp. 243–257). North-Holland.
Rudie K., Wonham W. M. (1992) Think globally, act locally: Decentralized supervisory control. IEEE Transactions on Automatic Control 37: 1692–1708
Thomas, W. (1995). On the synthesis of strategies in infinite games. In STACS 95, Proceedings of the Symposium on Theoretical Aspects of Computer Science (pp. 1–13).
Tripakis S. (2004) Undecidable problems of decentralized observation and control on regular languages. Information Processing Letters 90: 21–28
Walukiewicz, I. (2004). A landscape with games in the background. In Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science (LICS 2004) (pp. 356–366).
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Berwanger, D., Kaiser, Ł. Information Tracking in Games on Graphs. J of Log Lang and Inf 19, 395–412 (2010). https://doi.org/10.1007/s10849-009-9115-8
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DOI: https://doi.org/10.1007/s10849-009-9115-8