  Establishing causal relationships between actions and outcomes is fundamental
for accountable multi-agent decision-making. However, interpreting and
quantifying agents' contributions to such relationships pose significant
challenges. These challenges are particularly prominent in the context of
multi-agent sequential decision-making, where the causal effect of an agent's
action on the outcome depends on how other agents respond to that action. In
this paper, our objective is to present a systematic approach for attributing
the causal effects of agents' actions to the influence they exert on other
agents. Focusing on multi-agent Markov decision processes, we introduce
agent-specific effects (ASE), a novel causal quantity that measures the effect
of an agent's action on the outcome that propagates through other agents. We
then turn to the counterfactual counterpart of ASE (cf-ASE), provide a
sufficient set of conditions for identifying cf-ASE, and propose a practical
sampling-based algorithm for estimating it. Finally, we experimentally evaluate
the utility of cf-ASE through a simulation-based testbed, which includes a
sepsis management environment.
