Monopoly Market with Externality: an Analysis with Statistical Physics and Agent Based Computational Economics
Abstract
We explore the effects of social influence in a simple market model in which a large number of agents face a binary choice: 'to buy/not to buy' a single unit of a product at a price posted by a single seller (the monopoly case). We consider the case of 'positive externalities': an agent is more willing to buy if the other agents with whom he/she interacts make the same decision. We compare two special cases known in the economics literature as the Thurstone and the McFadden approaches. We show that they correspond to modeling the heterogenity in individual decision rules with, respectively, annealed and quenched disorder. More precisely the first case leads to a standard Ising model at finite temperature in a uniform external field, and the second case to a random field Ising model (RFIM) at zero temperature. Considering the optimisation of profit by the seller within the McFadden/RFIM model in the mean field limit, we exhibit a new first order phase transition: if the social influence is strong enough, there is a regime where, if the mean willingness to pay increases, or if the production costs decrease, the optimal solution for the seller jumps from one with a high price and a small number of buyers, to another one with a low price and a large number of buyers.
 Publication:

arXiv eprints
 Pub Date:
 November 2003
 arXiv:
 arXiv:condmat/0311096
 Bibcode:
 2003cond.mat.11096N
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Quantitative Finance  General Finance
 EPrint:
 20 pages, LaTeX2e, 5 figures. Presented at the 8th Annual Workshop on Economics with Heterogeneous Interacting Agents (WEHIA 2003, May 2931, Kiel)