A kinetic model for an agent based market simulation
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Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804
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School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804
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Received:
01 December 2014
Revised:
01 February 2015
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60K35, 91B26, 93A30.
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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.
Citation: Dieter Armbruster, Christian Ringhofer, Andrea Thatcher. A kinetic model for an agent based market simulation[J]. Networks and Heterogeneous Media, 2015, 10(3): 527-542. doi: 10.3934/nhm.2015.10.527
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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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