Two agents endowed with di erent individual conceptual spaces are engaged in a dialectic process to reach a common understanding. We model the process as a simple noncooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zero-sum structure. When the disagreement is widespread, the zero-sum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually agree to associate a region with the same concept end up rebranding it as a di erent concept. Finally, we document a conversers' dilemma: this last equilibrium outcome is Pareto-dominated by a cooperative solution that avoids retraction.