  We study a Bayesian coordination game where agents receive private
information on the game's payoff structure. In addition, agents receive private
signals on each other's private information. We show that once agents possess
these different types of information, there exists a coordination game in the
evaluation of this information. And even though the precisions of both signal
types is exogenous, the precision with which agents predict each other's
actions at equilibrium turns out to be endogenous. As a consequence, we find
that there exist multiple equilibria if the private signals' precision is high.
These equilibria differ with regard to the way that agents weight their private
information to reason about each other's actions.
