Choice under social influence : effects of learning behaviors on the collective dynamics

We consider a simple model in which a population of individuals with idiosyncratic willingnesses to pay must choose repeatedly either to buy or not a unit of a single homogeneous good at a given price. Utilities of buyers have positive externalities due to social interactions among customers. If the latter are strong enough, the system has multiple Nash equilibria, revealing coordination problems. We assume that individuals learn to make their decisions repeatedly. We study the performances along the learning path as well as at the customers’ reached equilibria, for different learning schemes based on past earned and/or forgone payoffs. Results are presented as a function of the price, for weak and strong social interactions. Pure reinforcement learning is shown to hinder convergence to the Nash equilibrium, even when it is unique. For strong social interactions, coordination on the optimal equilibrium through learning is reached only with some of the learning schemes, under restrictive conditions. The issues of the learning rules are shown to depend crucially on the values of their parameters, and are sensitive to the agents’ initial beliefs.