  Classical results of Decision Theory, and its extension to a multi-agent
setting: Game Theory, operate only at the associative level of information;
this is, classical decision makers only take into account probabilities of
events; we go one step further and consider causal information: in this work,
we define Causal Decision Problems and extend them to a multi-agent decision
problem, which we call a causal game. For such games, we study belief updating
in a class of strategic games in which any player's action causes some
consequence via a causal model, which is unknown by all players; for this
reason, the most suitable model is Harsanyi's Bayesian Game. We propose a
probability updating for the Bayesian Game in such a way that the knowledge of
any player in terms of probabilistic beliefs about the causal model, as well as
what is caused by her actions as well as the actions of every other player are
taken into account. Based on such probability updating we define a Nash
equilibria for Causal Games.
