p-Belief communication leading to a Nash equilibrium

A pre-play communication in the p-belief system is presented which leads to a Nash equilibrium of a strategic form game through messages. In the communication process each player predicts the other players' actions under his/her private information with probability at least p. The players communicate privately their conjectures through message according to the communication graph, where each player receiving the message learns and revises his/her conjecture. The emphasis is on that any topological assumptions on the communication graph are not required in the theorem.