Recent research on alcoholism explores the influence of family history and genetics on the risk of developing abuse or dependence. Endophenotypes and behavioral paradigms have been used to help detect genetic contributions to this disease. Electronic tasks, which can be considered video games, that provide alcohol as a reward in controlled environments have been developed to explore some of the behaviors and characteristics of individuals with or at risk for alcohol substance use disorders. One such game involves a progressive work paradigm where subjects receive larger or smaller alcohol rewards for completing the task. A generative model for this game is described along with the signal processing needed to characterize the subjects' behavior by system identification. Statistical performance of the algorithm is described and evaluated for the human data. Potential meanings of the different parameter values and the performance results are described.