Behavior strategies, mixed strategies and perfect recall

When perfect recall is not satisfied, the informational contents of mixed and behavior strategies differ and are more than what the information partition describes. First, we consider two kinds of additional information strategies may carry, and show that such information leads to the perfect recall refinement of a given information partition. This does not, however, imply that the strategies compensate fully for the lack of perfect recall. We give a necessary and sufficient condition on an information partition, called A-loss, for the informational content of mixed strategies to fully compensate for the lack of perfect recall. The informational content of behavior strategies never fully compensates.