The aim of the paper is to extend the syntax and semantics of the AG_n logic with components allowing the representation and verification of strategies in persuasion dialogue games. The AG_n logic was introduced to express beliefs and persuasive actions of agents, and then it was used to perform model checking in persuasive inter-agent communication. In this paper, we enrich AG_n by adapting strategy operators from Alternating-time Temporal Logic and adding new ones to allow reasoning about the success and persuasive power of dialogues.