Causal Games and Causal Nash Equilibrium

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.