Before revision:  Third, good aggregation can be achieved only if agents "anti-imitate" some neighbors: otherwise, equilibrium estimates are inefficiently confounded by "echoes. " Agents' stationary equilibrium learning rules incorporate past information by taking linear combinations of other agents' past estimates (as in the simple DeGroot heuristic), and we characterize the coefficients in these linear combinations .
After revision:  Third, good aggregation requires agents who understand correlations in neighbors' actions with the sophistication needed to concentrate on recent developments and filter out older, outdated information. In stationary equilibrium, agents' learning rules incorporate past information by taking linear combinations of other agents' past estimates (as in the simple DeGroot heuristic), and we characterize the coefficients in these linear combinations .