# Monopoly Market with Externality: an Analysis with Statistical Physics and ACE

*Jean-Pierre Nadal* (),
*Denis Phan*,
*Mirta B. Gordan* and
*Jean Vannimenus*

Additional contact information

Mirta B. Gordan: Leibniz-imag

Jean Vannimenus: ENS- LPS

Computational Economics from EconWPA

**Abstract:**
In this paper, we explore the effects of localised externalities introduced through interaction structures upon the properties of the simplest market model: the discrete choice model with a single homogeneous product and a single seller (the monopoly case). The resulting market is viewed as a complex interactive system with a communication network. Our main goal is to understand how generic properties of complex adaptive systems can enlighten our understanding of the market mechanisms when individual decisions are inter-related. To do so we make use of an ACE (Agent based Computational Economics) approach, and we discuss analogies between simulated market mechanisms and classical collective phenomena studied in Statistical Physics. More precisely, we consider discrete choice models where the agents are subject to local positive externality. We compare two extreme special cases, the McFadden (McF) and the Thurstone (TP) models. In the McF model the individuals' willingness to pay are heterogeneous, but remain fixed. In the TP model, all the agents have the same homogeneous part of willingness to pay plus an additive random (logistic) idiosyncratic characteristic. We show that these models are formally equivalent to models studied in the Physics literature, the McF case corresponding to a `Random Field Ising model' (RFIM) at zero temperature, and the TP case to an Ising model at finite temperature in a uniform (non random) external field. From the physicist's point of view, the McF and the TP models are thus quite different: they belong to the classes of, respectively,`quenched' and `annealed' disorder, which are known to lead to very different aggregate behaviour. This paper explores some consequences for market behaviour. Considering the optimisation of profit by the monopolist, 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 decreases, the optimal solution for the monopolist jumps from a solution with a high price and a small number of buyers, to a solution with a low price and a large number of buyers.

**Keywords:** Agent-Based Computational Economics; discret choices; consumers externality; complex adaptive system; phase transition; avalanches; interactions; hysteresis. (search for similar items in EconPapers)

**JEL-codes:** L1 D4 C6 (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-cmp, nep-dcm and nep-mic

**Date:** 2003-12-24

**Note:** Type of Document - pdf; prepared on Win2000; pages: 20. paper presented at the 8th Annual Workshop on Economics with Heterogeneous Interacting Agents, Kiel, May 29-31

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**Persistent link:** https://EconPapers.repec.org/RePEc:wpa:wuwpco:0312002

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