How to choose under social influence?

In this paper , we consider the simplest market situation where a population of heterogeneous individuals, subject to local positive externalities, have to choose repeatedly either to buy or not a unit of a single homogeneous good, at a price determined by a monopolist. We assume that the costumers have idiosyncratic willingness to pay, and suffer positive mutual influences. In previous work [16] we have shown that if the weight of the externalities is larger than a critical value, there are two Nash equilibria: one with a small fraction of buyers, another with a large fraction of buyers, the latter being the Pareto dominant optimum. The nature of this optimum is similar to that of the dominant Nash equilibrium in coordination games. It is worth to stress that these equilibria arise as a consequence of the externality for any distribution of the idiosyncratic component over the population, i.e. without having to assume a bimodal distribution of customers. From the monopolist’s point of view, determining the price that maximizes his profit under such conditions is a difficult problem, since he needs to anticipate which solution will be adopted by the customers. We have thus an entangled problem in which customers have to learn to select the best individual response in a game where (1) each one plays against all the others, and (2) customers and monoplist have to learn from each other. In this paper we analyze the learning problem of the customers under different conditions, and usin different learning schemes.