This article describes a simple two-player game which illustrates basic concepts of brinkmanship, to include calculations of probability and expected outcomes, and risk-taking profiles. The game befits a single 50-minute class period with introduction, gameplay, and discussion. The game can supplement the study of conflict from classic Cold War case studies of crisis bargaining, to arms control, or negotiating international protocols for global climate change such as the Paris Agreement. The Brinkmanship Game was developed for the seventh week of a 10-week graduate course called Game Theory and Decisionmaking: Exploring Strategic Situations. The course features a flipped classroom with class time devoted to experimentation, gameplay, and discussion of readings and games; lectures are online. The Brinkmanship Game would be appropriate for students in any advanced undergraduate or graduate level course in international relations, security studies, negotiation, or game theory. The Brinkmanship Game provides an active learning opportunity that can be valuable for encouraging students to come to their own understanding of concepts of mutual risk-taking. The authors have found the game to be effective in the classroom and hope it may prove valuable to those searching for ways to motivate students and to help them learn.