Bayesian Networks and Boundedly Rational Expectations

I present a framework for analyzing decision makers with an imperfect understanding of their environment's correlation structure. The decision maker faces an objective multivariate probability distribution (his own action is one of the random variables). He is characterized by a directed acyclic graph over the set of variables. His subjective belief filters the objective distribution through his graph, via the factorization formula for Bayesian networks. This belief distortion implies that the decision maker's long-run behavior may affect his perception of the consequences of his actions. Accordingly, I define a "personal equilibrium" notion of optimal choices. I show how recent models of boundedly rational expectations (as well as new ones, e.g. reverse causality) can be subsumed into this framework as special cases. Some general properties of the Bayesian-network representation of subjective beliefs are presented, as well as a "missing data" foundation.