Although evolutionary game theory has been popular in social sciences, we have seldom checked its utility as a tool in sociology. In this paper I argue that evolutionary game theory is a good tool with which we study evolution of certain types of social order, but that it has a limitation when we apply it to the study of evolution of the division of labor. To prove the argument, I first adopt a working definition of social order as a self-enforcing relationship between action and expectation. Then I adopt the fictitious play and best reply assumptions rather than the hardwired strategy and replicator dynamics assumptions, because the former are fitter for analysis of the self-enforcing relationship. Third, I claim that the core of the division of labor is the creation of new roles and build an evolutionary game theoretic framework of evolution of the division of labor. Finally, I point out that a limitation of evolutionary game theory in the study of evolution of the division of labor as social order is that it assumes a finite set of possible actions, while evolution of the division of labor accompanies new actions. This limitation, however, shows us where to attack to make a breakthrough.