An argument is presented for augmenting Gricean pragmatics with cognitively significant information about whether the participants in the interaction share the same goals, the same amount of information, and the degree of their awareness of both. The additions handle situations of competitive conversational exchanges, where the cooperative principle has been claimed to be inoperative, and show that cooperation underlies competitive exchanges as well. Some examples of competitive exchanges are examined, including witness cross-examination, sales pitches, propaganda, and lies.