Recently, game theory is widely used in sociological studies. But those studies usually postulate completeness of information which is uncommon in actual social phenomena. In this paper, I try to analyze constructed social reality, which characterized by uncertainty, intersubjectivity and factual constraint, with a game theory which can handle incompleteness of information. It is revealed that uncertainty of social reality, which means that there are infinite possible reality other than now established one, can be analyzed with "incomplete information game". Intersubjectivity has close relation to "common knowledge" concept in game theory, and is significant for the stability of social norms and rules. And "convention" concept which was used by Robert Sugden can be used to model the factual constraint of reality and stability of established reality. Though only a framework of game theoretical model of social reality is explored here, this study implicate that game theory is applicable to complicated and mean-oriented social phenomena.