  In this paper, we investigate the probabilistic variants of the strategy
logics ATL and ATL* under imperfect information. Specifically, we present novel
decidability and complexity results when the model transitions are stochastic
and agents play uniform strategies. That is, the semantics of the logics are
based on multi-agent, stochastic transition systems with imperfect information,
which combine two sources of uncertainty, namely, the partial observability
agents have on the environment, and the likelihood of transitions to occur from
a system state. Since the model checking problem is undecidable in general in
this setting, we restrict our attention to agents with memoryless (positional)
strategies. The resulting setting captures the situation in which agents have
qualitative uncertainty of the local state and quantitative uncertainty about
the occurrence of future events. We illustrate the usefulness of this setting
with meaningful examples.
