Two kinds of credibility will be distinguished, depending on the source of information. The first credibility, which will be called type I credibility, is regarding information about the player’s intention and the second credibility, which will be called type II credibility, is regarding information about the player’s hidden characteristic. The former problem of credibility occurs when a player makes a promise or a threat (in a certain period of time) that he will do something in the future and then something happens between the two points of time. Then, the promise or the threat may not be credible, since the player will not have the incentive to keep it any more. The latter occurs when the informed player tries to pretend to be a better type by exploiting the uninformativeness of the other player. Then, the message conveying his information may not be credible as long as the incentive to pretend exists.