  When designing or analyzing multi-agent systems, a fundamental problem is
responsibility ascription: to specify which agents are responsible for the
joint outcome of their behaviors and to which extent. We model strategic
multi-agent interaction as an extensive form game of imperfect information and
define notions of forward (prospective) and backward (retrospective)
responsibility. Forward responsibility identifies the responsibility of a group
of agents for an outcome along all possible plays, whereas backward
responsibility identifies the responsibility along a given play. We further
distinguish between strategic and causal backward responsibility, where the
former captures the epistemic knowledge of players along a play, while the
latter formalizes which players -- possibly unknowingly -- caused the outcome.
A formal connection between forward and backward notions is established in the
case of perfect recall. We further ascribe quantitative responsibility through
cooperative game theory. We show through a number of examples that our approach
encompasses several prior formal accounts of responsibility attribution.
