Game theory and sociology have nearly sixty years of relations. Published 54 years ago in the U.S., and this year in Poland, Thomas C. Schelling Strategies of conflict was an important step in the perception of game theory by sociologists. Despite initial signs of enthusiasm, especially in the 60s, and the publication of a number of major sociological works referring to the theory of games, in the end position of game-theoretical approach in sociology turns out to be marginal, even within rational choice sociology. Using the background of the history of the relationship between sociology and game theory, this paper analyzes factors that make game theory a potentially attractive tool for a sociologist, and the reasons why sociologists rarely use it.