  Concurrent stochastic games are an important formalism for the rational
verification of probabilistic multi-agent systems, which involves verifying
whether a temporal logic property is satisfied in some or all game-theoretic
equilibria of such systems. In this work, we study the rational verification of
probabilistic multi-agent systems where agents can cooperate by communicating
over unbounded lossy channels. To model such systems, we present concurrent
stochastic lossy channel games (CSLCG) and employ an equilibrium concept from
cooperative game theory known as the core, which is the most fundamental and
widely studied cooperative equilibrium concept. Our main contribution is
twofold. First, we show that the rational verification problem is undecidable
for systems whose agents have almost-sure LTL objectives. Second, we provide a
decidable fragment of such a class of objectives that subsumes almost-sure
reachability and safety. Our techniques involve reductions to solving
infinite-state zero-sum games with conjunctions of qualitative objectives. To
the best of our knowledge, our result represents the first decidability result
on the rational verification of stochastic multi-agent systems on infinite
arenas.
