In international security, there are many cases of inter-group conflict where violence persists and conflict-oriented policies dominate at the expense of a more mutually beneficial allocation of societal goods. What are the barriers to successful negotiation in such scenarios, and why are conflict management policies difficult to achieve? Most studies of conflict focus on highlevel political, economic, or sociological causes; however, psychological influences on decision-making, such as threat and personal motivation, play a large role in impeding conflict resolution or negotiation. In this paper, we analyze the psychological dynamics of threat perception and vested interests on the persistence or desistence of conflict. Threat perception can cause sudden and dramatic shifts in opinion and political choices, an effect which can be further amplified by media reporting. Leaders with a vested personal interest in continued conflict-"spoilers"-can manipulate this phenomenon to derail a peace process. We present a dynamic game theoretic framework of parallel intergroup negotiation and conflict models that incorporates this feedback between threat perception, motivations, leadership decisions, and the success of negotiations, explicitly representing the psychological components of conflict. A prototype implementation is used in empirical simulations to identify cases of conflict persistence and desistence.