Learning in Networks with Idiosyncratic Agents

Abstract

Individuals are slow to update their beliefs and may respond to new information in idiosyncratic ways. Since their beliefs affect the choices of those they are linked with, the idiosyncrasies that affect their capacity to learn information also affect the accumulation of information across society. I study how an individual’s slowness to respond to new information (due to status quo bias) and idiosyncratic ways of responding to new information (due to overreaction or frustration) affect (a) the ability of society to reach an agreement (b) the ability of society to reach the correct agreement and (c) the speed with which such an agreement is reached. I derive sufficient conditions for convergence in beliefs in the form of network dependent upper bounds on idiosyncrasies for all networks of individuals with heterogeneous biases, placing heterogeneous weights on their neighbours. Then, I highlight that the absence of very connected agents is not sufficient to ensure that beliefs converge to the truth when idiosyncrasies also change with network size. I also show how biases can affect the speed with which societies learn by deriving status quo bias dependent upper bounds on bottlenecks for regular networks. I illustrate how this can be used to bound mixing times and how such analyses can be used to understand and tackle norm persistence. Finally, I simulate the model on real world and artificially generated networks and find that these results are validated.