Players have uncertainty over both an external random variable -- such as a security price -- and over each other's beliefs. We study agents’ subjective expectations of the weighted average of others' subjective expectations . . . of the weighted average of others' subjective expectations of the external random variable. The weights involved can be viewed as a network. By relating these iterated average expectations to a Markov chain, we characterize their limit properties, generalizing prior results on games with common priors and on complete-information network games. We then apply the conclusions to study coordination games, over-the-counter financial markets, the possibility of rationalizable trade, and the robustness of equilibrium.

 This is joint work with Stephen Morris (Princeton).