We investigate the interrelation between graph searching games and games with
imperfect information. As key consequence we obtain that parity games with
bounded imperfect information can be solved in PTIME on graphs of bounded
DAG-width which generalizes several results for parity games on graphs of
bounded complexity. We use a new concept of graph searching where several cops
try to catch multiple robbers instead of just a single robber. The main
technical result is that the number of cops needed to catch r robbers
monotonously is at most r times the DAG-width of the graph. We also explore
aspects of this new concept as a refinement of directed path-width which
accentuates its connection to the concept of imperfect information
