“Learning in Local Networks” by Wei Li
University of British Columbia
University of Washington
Agents in a network want to learn the true state of the world from their own signals and reports from immediate neighbors. Each agent only knows her local network, consisting of her immediate neighbors and any connections among them. In each period, every agent updates her own estimates about the state distribution based on perceived new information. She also forms estimates about each neighbor’s estimates given the new information she thinks the neighbor has received. Whenever a neighbor’s report differs from what the agent thinks he should report, the agent attributes the difference to new information. Agents learn correctly in any network if their information structures are partitional. They can also do so for more general information structures if the network is a social quilt, a tree-like union of fully connected subnetworks. Otherwise, agents may fail to learn despite an arbitrarily large number of correct signals.