The paper proposes an extension of the modal logic
with operators for reasoning about different types of strategies which agents may adopt in order to win a dialogue game. We model agent communication using the paradigm of formal systems of dialogues and in particular, a system proposed by Prakken. In the paper, the traditional notion of a winning strategy is extended with a notion of a strategy giving a
for success and a notion of a strategy giving a
of chances for victory. Then, using the framework of Alternating-time Temporal Logic (ATL) we specify
operators which allow the investigation of the dialogical strategies.