Earlier Version

Partial-observation stochastic games: How to win when belief fails

K. Chatterjee, L. Doyen, in:, Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2012, p. 6280436.


Conference Paper | Published | English
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Abstract
We consider two-player stochastic games played on finite graphs with reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1), or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, the players (a) may not be allowed to use randomization (pure strategies), or (b) may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) may use full randomization. Our main results for pure strategies are as follows. (1) For one-sided games with player 1 having partial observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almostsure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete. (2) For one-sided games with player 2 having partial observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least non-elementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibits serious flaws in previous results of the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.
Publishing Year
Date Published
2012-08-23
Proceedings Title
Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science
Acknowledgement
This work was partially supported by FWF Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.
Article Number
6280436
Conference
LICS: Logic in Computer Science
Conference Location
Dubrovnik, Croatia
Conference Date
2012-06-25 – 2012-06-28
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Cite this

Chatterjee K, Doyen L. Partial-observation stochastic games: How to win when belief fails. In: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. IEEE; 2012:6280436. doi:10.1109/LICS.2012.28
Chatterjee, K., & Doyen, L. (2012). Partial-observation stochastic games: How to win when belief fails. In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science (p. 6280436). Dubrovnik, Croatia: IEEE. https://doi.org/10.1109/LICS.2012.28
Chatterjee, Krishnendu, and Laurent Doyen. “Partial-Observation Stochastic Games: How to Win When Belief Fails.” In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, 6280436. IEEE, 2012. https://doi.org/10.1109/LICS.2012.28.
K. Chatterjee and L. Doyen, “Partial-observation stochastic games: How to win when belief fails,” in Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, Dubrovnik, Croatia, 2012, p. 6280436.
Chatterjee K, Doyen L. 2012. Partial-observation stochastic games: How to win when belief fails. Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science 6280436.
Chatterjee, Krishnendu, and Laurent Doyen. “Partial-Observation Stochastic Games: How to Win When Belief Fails.” Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2012, p. 6280436, doi:10.1109/LICS.2012.28.

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