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The aim of the paper is to extend the syntax and semantics of the AGn logic with components allowing the representation and verification of strategies in persuasion dialogue games. The AGn 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 AGn by adapting strategy operators from Alternating-time Temporal Logic and adding new ones to allow reasoning about the success and persuasive power of dialogues.