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This paper considers a epistemic game-theoretic model of group identification which describes the evolving process of a collective action rule of the members in a social group. Group identity describes that the solutions to "who we are'' and "what we are'' questions among the members in a group. Given a social group consisting its members, the group identity is a common action rule with respect to their rival group. Under the assumption of interaction costs and results of information convergence, we construct a knowledge foundation for group identity and group identification. Our results show that under a finite state space, group identification can be implemented among in-group members via finite information revision steps if the two conditions hold: (1) the members of a group can communicate with each other for increasing their knowledge, and (2) there is a nonzero cost generating by the interaction between ingroup members and outsiders. Furthermore, we show that on a probability space, a generalized group identification is equivalent to a discrete-time martingale process, which permits that group identification can be reached under the infinite state space.