A Bayesian communication in the p-belief system is presented which leads to a Nash equilibrium of a strategic form game through messages as a Bayesian updating process. In the communication process each player is an expectations maximiser, and he/she predicts the other players? actions under his/her private information with the conditional probability at least his/her belief. Each player communicates privately his/her conjecture through message according to the communication graph, where the player receiving the message learns and revises his/her conjecture. We show that the players? conjectures regarding the future beliefs converge to a mixed strategy Nash equilibrium of a game in the long run communication. The emphasis is on that each player predicts the others? actions under his/her private information consisting of rough sets.