The cease-and-desist commitment (CCP, a mechanism equivalent to a Consent Decree in the United States) is an agreement between the Administrative Counsel of Concurrence Defense (CADE) and an anticompetitive firm, aiming to cease the investigated practice in a certain period of time. During this agreement, there is a withdraw of the lawsuit. If the firm hasn't been respected the CCP, fines and reputation sanctions can be applied. Considering that the CCP utilization is still new in Brazil as well the literature about the theme, the objective of this paper is to analyze the conditions for a firm make a CCP, in a game with incomplete information. The results indicate that: the firms should follow the CCP as bigger were the loss of reputation and fines, and smaller the infraction profits against the normal profits; the antitrust authority should offer the CCP when the benefits of this proposal were bigger than the losing of the firm; the antitrust authority should offer the CCP when there is a belief that the firm is low cost type.