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The influence of family history and genetics on the risk for the development of abuse or dependence is a major theme in alcoholism research. Recent research have used endophenotypes and behavioral paradigms to help detect further genetic contributions to this disease. Electronic tasks, essentially video games, which provide alcohol as a reward in controlled environments and with specified exposures have been developed to explore some of the behavioral and subjective characteristics of individuals with or at risk for alcohol substance use disorders. A generative model (containing parameters with unknown values) of a simple game involving a progressive work paradigm is described along with the associated point process signal processing that allows system identification of the model. The system is demonstrated on human subject data. The same human subject completing the task under different circumstances, e.g., with larger and smaller alcohol reward values, is assigned different parameter values. Potential meanings of the different parameter values are described.