Wendt (1999) identifies Hobbesian, Lockean, and Kantian strategic cultures drawn from Western political philosophy, which inform the realist (Hobbesian), liberal (Lockean), and constructivist (Kantian) schools of international relations theory. He privileges the cultural level of analysis as the deepest level of order under the condition of anarchy (politics without government) and argues that roles at the cultural level inform the institutional level of rules and the material level of power. He leaves unspecified the roles of enemy, rival, and friend that differentiate these strategic cultures plus the strategic interaction mechanisms of role conflict and role transition that account for the evolution of anarchy from one strategic culture to another along three dimensions of international order: military, economic, and political. We apply binary role theory to these puzzles, specify as formal models the possible nonlinear patterns identified by Wendt, and apply them to empirical puzzles identified by Wohlforth et al. (2007) and Goertz, Diehl, and Balas (2016) regarding how and why states transition to appeasement and bandwagon strategies from hegemonic and balancing strategies as social mechanisms of international order. We pay particular attention to agent-level processes of internalization that explain role transition across different military, economic, and political dimensions of international order.