  Causal games are probabilistic graphical models that enable causal queries to
be answered in multi-agent settings. They extend causal Bayesian networks by
specifying decision and utility variables to represent the agents' degrees of
freedom and objectives. In multi-agent settings, whether each agent decides on
their policy before or after knowing the causal intervention is important as
this affects whether they can respond to the intervention by adapting their
policy. Consequently, previous work in causal games imposed chronological
constraints on permissible interventions. We relax this by outlining a sound
and complete set of primitive causal interventions so the effect of any
arbitrarily complex interventional query can be studied in multi-agent
settings. We also demonstrate applications to the design of safe AI systems by
considering causal mechanism design and commitment.
