A Lattice Theory for Solving Games of Imperfect Information

In this paper, we propose a fixed point theory to solve games of imperfect information. The fixed point theory is defined on the lattice of antichains of sets of states. Contrary to the classical solution proposed by Reif [Rei84], our new solution does not involve determinization. As a consequence, it is readily applicable to classes of systems that do not admit determinization. Notable examples of such systems are timed and hybrid automata. As an application, we show that the discrete control problem for games of imperfect information defined by rectangular automata is decidable. This result extends a result by Henzinger and Kopke in [HK99].