Randomized Strategies in Regular Games with Imperfect Information Are Challenging

Regular games with imperfect information, despite their nice structural properties and the existence of a finite bisimulation in their information tree, do not admit a similar reduction for the synthesis of randomized strategies as in the case of partial-observation games à la Reif. The synthesis problem for randomized strategies in regular games is decidable for reachability and Büchi objectives, but the reductions that worked in games à la Reif no longer hold.