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Partial-Observation Stochastic Games: How to Win when Belief Fails
du groupe Graphes et Logique

Date 2011-12-06  11:00-12:00
TitrePartial-Observation Stochastic Games: How to Win when Belief Fails  
RésuméWe consider two-player stochastic games played on finite graphs with reachability (and Buechi) objectives where the first player tries to ensure a target state to be visited (or visited infinitely often) 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 to 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, or two-sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Our main results for pure strategies are as follows: (1) For one-sided games with player 2 perfect observation we show that (in contrast to full randomized strategies) belief-based strategies are not sufficient, and we present an exponential upper bound on memory both for almost-sure 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 1 perfect 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 in the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed. 
Lieusalle 76 
OrateurLaurent Doyen 

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