Global Games with Noisy Information Sharing

Global games form a subclass of games with incomplete information where a set of agents decide actions against a regime with an underlying fundamental $\theta$ representing its power. Each agent has access to an independent noisy observation of $\theta$. In order to capture the behavior of agents in a social network of information exchange we assume that agents share their observation in a noisy environment prior to making their decision. We show that global games with noisy sharing of information do not admit an intuitive type of threshold policy which only depends on agents' belief about the underlying $\theta$. This is in contrast to the existing results on the threshold policy for the conventional set-up of global games. Motivated by this result, we investigate the existence of equilibrium strategies in a more general collection of threshold-type policies and show that such equilibrium strategies exist and are unique if the sharing of information happens over a sufficiently noisy environment.