Private sunspots in games of coordinated attack

I endogenize the probability of self-fulfilling outcomes in a game where the only uncertainty comes from extrinsic sunspots. There is a group of players wishing to coordinate on the same action and another player—the regime defender—whose action affects the payoff from coordination. The coordinating players' actions can be based on a sunspot state, which, unlike in the classic sunspot approach, is observed with a small, idiosyncratic noise (a private sunspot). I show how private sunspots, combined with the action of the regime defender, can be used to derive a unique coordination probability in any equilibrium where sunspots influence actions. I show how this approach can be used to determine the probability of a sunspot-driven bank run.