A Single-Judge Solution to Beauty Contests

We show that the equilibrium policy rule in beauty-contest models is equivalent to that of a single agent's forecast of the economic fundamental. This forecast is conditional on a modified information process, which simply discounts the precision of idiosyncratic shocks by the degree of strategic complementarity. The result holds for any linear Gaussian signal process (static or persistent, stationary or non-stationary, exogenous or endogenous), and also extends to network games. Theoretically, this result provides a sharp characterization of the equilibrium and its properties under dynamic information. Practically, it provides a straightforward method to solve models with complicated information structures.