In this paper, we present computational models for generating influence that allow story managers to shape players' decisions in interactive narrative experiences. Our approach uses concepts from social psychology, discourse analysis, and natural language generation. We describe an abstract formalism to operationalize tools of social psychological influence described by Cialdini (Influence: The Psychology of Persuasion, New York, NY, USA: Harper-Collins, 1998) and evaluate two example implementations that enable a storytelling system to generate influence on the fly (with varying degrees of success), thereby adapting stories to realize goals specified by authors. These implementations are used in an interactive story where influence is generated dynamically as players' experiences unfold. We present the results of a user study to characterize the effectiveness of these models. Results did not indicate the presence of any significant differences in players' sense of control over the story with, or without, the use of influence. Further, the use of influence resulted in a set of stories experienced by players that more closely matched the author's goals.