In many settings, machine learning models may be used to inform decisions that impact individuals or entities who interact with the model. Such entities, or agents, may game model decisions by manipulating their inputs to the model to obtain better outcomes and maximize some utility. We consider a multi-agent setting where the goal is to identify the "worst offenders:" agents that are gaming most aggressively. However, identifying such agents is difficult without knowledge of their utility function. Thus, we introduce a framework in which each agent's tendency to game is parameterized via a scalar. We show that this gaming parameter is only partially identifiable.