We introduce a model of a cyclic game. Designed to take advatange of the recurring nature of certain economic and social situations, a cyclic game differs from an extensive form game in that a cyclic game does not necessarily have an end. The same situations, although with different players may be repeated infintely often. This feature makes a cyclic game essentially finite, although it may have an infinite number of players and may be unending. We provide an example showing that, even though a cyclic game has, in a sense, perfect information, it may not have an equilibrium in pure strategies. We also provide an existence of equilibrium theorem and illustrate the application of our model to an oligopolistic industry.
