Naive Learning Through Probability Overmatching

We analyze boundedly rational updating in a repeated interaction network model with binary actions and binary states. Agents form beliefs according to discretized DeGroot updating and apply a decision rule that assigns a (mixed) action to each belief. We first show that under weak assumptions, random decision rules are sufficient to achieve agreement in finite time in any strongly connected network. Ourmain result establishes that naive learning can be achieved in any large strongly connected network. That is, if beliefs satisfy a high level of inertia, then there exist corresponding decision rules coinciding with probability overmatching such that the eventual agreement action matches the true state, with a probability converging to one as the network size goes to infinity.