A concept of competitive equilibrium is proposed for a game. The following three reasons are given, proving that this is really a generalization of the concept used in economic theory: (i) The mathematical definition is the same; (ii) an existence theorem is proved in the same way; (iii) when the number of players becomes very large, in a suitable way, the core and the equilibrium are the same. The concept and utilization of a characteristic function, a generalization of the one defined by von Neumann and Morgenstern, form the basis of this paper.