Abstract
We study a coordination game where players choose what information to acquire about payoffs prior to the play of the game. We allow general information acquisition technologies, modeled by a cost functional defined on information structures. A cost functional satisfies continuous choice if players choose a continuous decision rule even in a decision problem with discontinuous payoffs. If continuous choice holds, there is a unique equilibrium; if it fails, there are multiple equilibria. We show how continuous choice captures the idea that it is sufficiently harder to distinguish states that are close to each other relative to far away states.
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