We study learning in Bayesian games (or games with differentialinformation) 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 alsoare allowed to be completely irrational in some states of the world.We show that bounded rational players by repetition can reach a limitfull information BNE outcome. We also prove the converse, i.e., givena limit full information BNE outcome, we can construct a sequence ofbounded rational plays that converges to the limit full informationBNE outcome.