Monopoly Market with Externality: an Analysis with Statistical Physics and ACE
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.
|Date of creation:||24 Dec 2003|
|Date of revision:|
|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|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
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- Denis Phan & Stephane Pajot & Jean-Pierre Nadal, 2003. "The Monopolist's Market with Discrete Choices and Network Externality Revisited: Small-Worlds, Phase Transition and Avalanches in an ACE Framework," Computing in Economics and Finance 2003 150, Society for Computational Economics.
- Weisbuch, Gérard & Stauffer, Dietrich, 2003. "Adjustment and social choice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 651-662.
- Jean-Philippe Bouchaud, 2000. "Power-laws in economics and finance: some ideas from physics," Science & Finance (CFM) working paper archive 500023, Science & Finance, Capital Fund Management.
- Alan Kirman, 1997. "The economy as an evolving network," Journal of Evolutionary Economics, Springer, vol. 7(4), pages 339-353.
- Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
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