Jon Elster studied the fallacy of composition in virtue of modal logic, by defining it as the non-universalizability of predicate. He made it possible to connect the modal fallacy of composition with game theory, based on which he came up with a new theory of social contradictions. Through the combination of social contradictions and social choices of intentional agents, Elster described the mental and practical actions of cognitive agents based on methodological individualism. He put forward counterfinality and suboptimality, and his work pioneers in the research of social science in virtue of logical methods. Following Elster’s analytic approach, we can construct models for the dilemmas analogous to paradoxes in the actions. We hope this research can contribute to reveal the internal mechanisms of social competitions and contradictions, and open up a feasible path to avoid vicious competitions and resolve social contradictions.