We build a workable game of common-property resource extraction under rational Bayesian learning about the reproduction prospects of a resource. We focus on Markov-perfect strategies under truthful revelation of beliefs. For reasonable initial conditions, exogenously shifting the prior beliefs of one player towards more pessimism about the potential of natural resources to reproduce, can create anti-conservation incentives. The single player whose beliefs have been shifted towards more pessimism exhibits higher exploitation rate than before. In response, all other players reduce their exploitation rates in order to conserve the resource. However, the overall conservation incentive is weak, making the aggregate exploitation rate higher than before the pessimistic shift in beliefs of that single player. Due to this weakness in strategic conservation responses, if the number of players is relatively small, then in cases with common priors, jointly shifting all players'beliefs towards more pessimism exacerbates the commons problem.