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Two-player, turn-based, stochastic games with reachability conditions are considered, where the maximizer has no information (he is blind) and is restricted to deterministic strategies whereas the minimizer is perfectly informed. We ask the question of whether the game has maxmin value of 1 in other words we ask whether for all \(\epsilon >0\) there exists a deterministic strategy for the (blind) maximizer such that against all the strategies of the minimizer, it is possible to reach the set of final states with probability larger than \(1-\epsilon \). This problem is undecidable in general, but we define a class of games, called leaktight half-blind games where the problem becomes decidable. We also show that mixed strategies in general are stronger for both players and that optimal strategies for the minimizer might require infinite-memory.

This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transitions.

International audience; We introduce stochastic priority games - a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination of the classical discount payoff and of a limit payoff evaluating the performance at infinity. Shapley games and parity games are special extreme cases of priority games.

International audience; This paper examines two players' turn-based perfect-information games played on infinite graphs. Our attention is focused on the classes of games where winning conditions are boolean combinations of the following two conditions: (1) the first one states that an infinite play is won by player $0$ if during the play infinitely many different vertices were visited, (2) the second one is the well known parity condition generalized to a countable number of priorities. We show that, in most cases, both players have positional winning strategies and we characterize their respective winning sets. In the special case of pushdown graphs, we use these results to show that the sets of winning positions are regular and we show how to compute them as well as positional winning strategies in exponential time.

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.