Collaborative stories

Can a game help you write a meaningful story with others? Academic discussion of collaborative story-writing games usually contains reference to Surrealist game Exquisite Corpse, known to many as Consequences. In it, a game rule prohibits players, writing in turn, from reading most of the story written before their contribution. This rule promotes a fragmented form of narrative which, although often inventive and entertaining, does not often fulfill the normal requirements of a story.