We study learning in Bayesian games (or games with differential information) with an arbitrary number of bounded rational players, i.e., players who choose approximate best response strategies [approximate Bayesian Nash Equilibrium (BNE) strategies] and who also are allowed to be completely irrational in some states of the world. We show that bounded rational players by repetition can reach a limit full information BNE outcome. We also prove the converse, i.e., given a limit full information BNE outcome, we can construct a sequence of bounded rational plays that converges to the limit full information BNE outcome.

We generalize results of earlier work on learning in Bayesian games by allowing players to make decisions in a nonmyopic fashion. In particular, we address the issue of nonmyopic Bayesian learning with an arbitrary number of bounded rational players, i.e., players who choose approximate best-response strategies for the entire horizon (rather than the current period). We show that, by repetition, nonmyopic bounded rational players can reach a limit full-information nonmyopic Bayesian Nash equilibrium (NBNE) strategy. The converse is also proved: Given a limit full-information NBNE strategy, one can find a sequence of nonmyopic bounded rational plays that converges to that strategy.