Real-world games often involve both structured and unstructured interaction. For the clearly delineated moves and countermoves in such games, a non-cooperative game model can be used. But for unstructured interaction, when the moves are more fluid and free-form, a cooperative game model is more natural. This paper develops a hybrid non-cooperative/cooperative formalism, called the biform game model, designed for the study of such mixed games. As a test of the biform model, it is applied to the analyses of monopoly and perfect competition.