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. Our main 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.

Funding: I. Arieli acknowledges support from the Ministry of Science and Technology [Grant 19400214] and the Israel Science Foundation [Grant 2029464]. Y. Babichenko acknowledges support from the Israel Science Foundation [Grant 2021296]. M. Mueller-Frank acknowledges the financial support of the Spanish Ministry of Science, Innovation, and Universities [Grant ECO2015-63711-P] and of the Department of the Economy and Knowledge of the Generalitat de Catalunya [Grant 2017 SGR 1244].