We prove existence and purification results for strategic environments possessing a product structure that includes classes of large games, stochastic games, and models of endogenous institutions. Applied to large games, the results yield existence of pure-strategy equilibria allowing for...

We study elections in which two candidates poll voters about their preferred policies before taking policy positions. In the essentially unique equilibrium, candidates who receive moderate signals adopt more extreme platforms than their information suggests, but candidates with more extreme...