In this paper we propose a new persuasion dialogue game for agent communication. We show how this dialogue game is modeled by a framework based on social commitments and arguments. Called Commitment and Argument Network (CAN), this framework allows us to model communication dynamics in terms of actions that agents apply to commitments and in terms of argumentation relations. This dialogue game is specified by indicating its entry conditions, its dynamics and its exit conditions. In order to solve the problem of the acceptance of arguments, the protocol integrates the concept of agents’ trustworthiness in its specification. The paper proposes a set of algorithms for the implementation of the persuasion protocol and discusses their termination, complexity and correctness.