Entanglement between Demand and Supply in Markets with Bandwagon Goods

TL;DR

This paper analyzes how demand and supply interact in markets with bandwagon effects, revealing a complex 'curse of coordination' where optimal pricing strategies depend on customer coordination near critical demand thresholds.

Contribution

It introduces a detailed mathematical model linking market demand with social coordination effects, extending concepts from physics and social science.

Findings

Demand can have multiple values at the same price due to positive externalities.

Optimal pricing strategies are near critical points where demand shifts occur.

The model relates market behavior to the Random Field Ising Model and Schelling's social models.

Abstract

Whenever customers' choices (e.g. to buy or not a given good) depend on others choices (cases coined 'positive externalities' or 'bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one -- in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model and to a model introduced in social sciences by T C Schelling in the 70's.