For a long period of time，game theory has traditionally relied upon a tacit and “classical” set of modeling paradigms. In order to reach equilibrium，classical game theorists need to set some limits for every model，which make the implied assumptions of game theory. However，games that happen in the real world are not confined to a given circumstance. Game players are often influenced by the outside situation. And people need to define the situation and identify other actors before they develop strategies. It leaves open of the question that what will happen to the game models if we take into consideration the factors like definition of situation and identity？Definition of situation can influence both the basic environment of interaction and identification of other actors. Defining situation in a different way，game players take different logic of behavior and strategies，which will make a huge difference in approach-developing in the game. This paper reviews the logic and modeling paradigms of classical game theory and points out their implied assumptions and possible ‘blind spots’. It also reviews key conceptions like definition of situation and identity in the theory of social interactionism and discuss the possibility of introducing them into game theory.