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We examine the relationship between private capabilities and war in a new class of crisis bargaining games. While crisis bargaining games typically only considers outcomes of war or a peaceful bargain, we assume that actors can also engage in a wide range of low-level, costly policy options that shape final political outcomes in their favor (representing actions like sanctions, arming, cyberattacks, etc.). This modeling modification undermines seminal theoretical results that previously identify a positive relationship between a state’s private capabilities for war and both that state’s final expected utility and the overall likelihood of war in the game; we show that these relationships no longer hold generally when a state’s private capabilities affect both war efficacy and low-level operation efficacy. Using the tools of Bayesian mechanism design, we establish the general conditions that define the relationships between private abilities, war, and expected utilities for what we call “flexible-response crisis bargaining games.”