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.