A kinetic model for an agent based market simulation

Dieter Armbruster; Christian Ringhofer; Andrea  Thatcher

doi:10.3934/nhm.2015.10.527

Article Contents

2015, Volume 10, Issue 3: 527-542. Doi: 10.3934/nhm.2015.10.527

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A kinetic model for an agent based market simulation

1.
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804
2.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804

Received: December 2014

Revised: February 2015

Published: September 2015

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Abstract

A kinetic model for a specific agent based simulation to generate the sales curves of successive generations of high-end computer chips is developed. The resulting continuum market model consists of transport equations in two variables, representing the availability of money and the desire to buy a new chip. In lieu of typical collision terms in the kinetic equations that discontinuously change the attributes of an agent, discontinuous changes are initiated via boundary conditions between sets of partial differential equations. A scaling analysis of the transport equations determines the different time scales that constitute the market forces, characterizing different sales scenarios. It is argued that the resulting model can be adjusted to generic markets of multi-generational technology products where the innovation time scale is an important driver of the market.

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Mathematics Subject Classification: 60K35, 91B26, 93A30.

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