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ATL + is a variant of alternating-time temporal logic that does not have the expressive power of full ATL * , but still allows for expressing some natural properties of agents. It has been believed that verification with ATL + is Δ P 3 -complete for both memoryless agents and players who can memorize the whole history of the game. In this paper, we show that the latter result is not correct. That is, we prove that model checking ATL + for agents that use strategies with memory is in factdoi:10.3233/aic-2010-0481 fatcat:isgy66f2n5b53gonkqfhatgmxu