This paper reviews some major concepts in game theory and indicates how they may apply to marketing science. The theory of games provides a framework for addressing problems of competitive strategies and of buyer-seller interactions. These issues are important in studying industrial markets where there are a small number of buyers as well as for studying how to incorporate knowledgeable, active competitors into consumer marketing mix models. Few marketers have seen much benefit in the past from developments in game theory. This is partly because of the historical preoccupation of game theorists with complete information, zero sum games. The richer area of games of incomplete information may have much more to offer the marketing scientist. In this paper we review how game-theoretic approaches (interactive models) differ from most previous approaches, which are optimizing and asymmetric. We then look at how these alternative approaches apply to two problem areas - competitive entry and bargaining. Then we review potential applications of game theory in marketing and the value of applying marketing science approaches in game theory. We conclude with a perspective on future developments in this field.