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Russia launched its war against Ukraine in early 2022, expecting a rapid victory. Ukrainian resistance in the ensuing months not only dispelled any notion of that outcome but has raised the possibility that Ukraine might win the war. Russian President Vladimir Putin has staked everything on this invasion, and he is unlikely to accept defeat without exhausting significant resources at his disposal. This dynamic between Ukrainian momentum and Russia's desperation has raised concerns that Russia might resort to nuclear escalation to turn the tide of the war. Given this reality, U.S. policymakers and planners must consider appropriate responses. In this report, the authors attempt to identify such responses and levers using a game theory approach to the situation. They do so by first providing an overview of Russia's nuclear doctrine and capabilities, considering its discourse on nuclear escalation and declaratory policies relevant to the possible use of nonstrategic nuclear weapons (NSNWs). They then look at Russia's nuclear escalation through the lens of game theory, examining which potential levers for shifting decisionmaking and outcomes exist in the game. Finally, they assess how a particularly relevant historical example, the Kargil War, sheds light on possible U.S. responses for avoiding escalation without conceding to adversary demands.