Abstract: Despite an ongoing policy debate within the United States about the value of alliances, research suggests that the complex network of security relationships that the United States and other major patrons have established since the end of World War II have important and understudied implications for a wide range of bargaining and cooperation dynamics. To tackle this pressing policy problem, this project delves into the strategic behavior of states in alliances with nuclear security guarantors or patrons. It asks two main questions. First, how do nuclear umbrellas produce risky security outcomes – namely, moral hazard – through which client states might recklessly entrap nuclear patrons into military engagement with adversaries? And second, how can nuclear patrons design alliances to induce restraint among client states, prevent these risky outcomes, and yield positive dividends for the international system? To explore these questions, we pursue three lines of inquiry. First, we develop a new theoretical framework that explores the duality of nuclear umbrellas – their burdens and their benefits. Second, we employ a series of large-n statistical tests exploring the relationship of the United States and other patron states with their various treaty allies and adversaries over time. Third, we examine this logic and mechanisms for both recklessness and restraint through a series of in-depth case studies, including Taiwan and NATO. The manuscript concludes with valuable insights and recommendations for policymakers focused on grand strategy and the broad network of U.S. alliances.