Both Vito and Michael believed in fooling adversaries into believing that they were weaker than they appeared--the better to have them relax their guard. Vito's apparent weakness was in rising from his sick bed to call off the war, and in agreeing to provide police/political protection to the drugs business in the East. But his objective was to strengthen his family by bringing Michael safely back to the US as his successor. Michael pretended not to react to Barzini's incursions into his territories, and to agree to a meeting with Barzini. His objective was to get Barzini and the other Dons to lower their guard by regarding him as a no-account. Both Vito and Michael succeeded.