In this chapter I present results from a mathematical formalization of intensity theory. I apply tools from game theory to analyze the dynamics of electoral competition when voters vary in how much they care about policy and when candidates do not know which voters care more and less intensely. I show that candidates for office choose policy platforms as a function of the size and intensity of opposing policy coalitions. Candidates sometimes set policy with an intense minority even though they know that a less-intense majority wants the opposite policy. But they also sometimes choose not to frustrate majorities even with an intense minority.