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September  2015, 10(3): 527-542. doi: 10.3934/nhm.2015.10.527

A kinetic model for an agent based market simulation

Dieter Armbruster 1, , Christian Ringhofer 1, and  Andrea Thatcher 2,

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, United States

Received  December 2014 Revised  February 2015 Published  July 2015

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.
Keywords: agent based simulations, Kinetic theory, multi-generational technology products., market models.
Mathematics Subject Classification: 60K35, 91B26, 93A3.
Citation: Dieter Armbruster, Christian Ringhofer, Andrea Thatcher. A kinetic model for an agent based market simulation. Networks & Heterogeneous Media, 2015, 10 (3) : 527-542. doi: 10.3934/nhm.2015.10.527
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show all references

References:
[1]

Advances in Complex Systems, 16 (2013), 1350028, 33pp. doi: 10.1142/S0219525913500288.  Google Scholar

[2]

SIAM J. Appl. Math, 66 (2006), 896-920. doi: 10.1137/040604625.  Google Scholar

[3]

Mathematical Models in Marketing, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 351-253. doi: 10.1007/978-3-642-51565-1_107.  Google Scholar

[4]

Theoretical Physics and Philosophical Problems, Vienna Circle Collection, 5 (1974), 13-32. doi: 10.1007/978-94-010-2091-6_2.  Google Scholar

[5]

Springer-Verlag, 1994. doi: 10.1007/978-1-4419-8524-8.  Google Scholar

[6]

J. Nonlinear Sci., 24 (2014), 93-115. doi: 10.1007/s00332-013-9185-2.  Google Scholar

[7]

J. Stat. Phys., 154 (2014), 751-780. doi: 10.1007/s10955-013-0888-4.  Google Scholar

[8]

Behavioral sciences, 37 (1992), 190-214. Google Scholar

[9]

Cambridge University Press, 2002. doi: 10.1017/CBO9780511791253.  Google Scholar

[10]

Manufacturing & Service Operations Management, 15 (2013), 343-360. doi: 10.1287/msom.2013.0430.  Google Scholar

[11]

Oxford University Press, 2014. Google Scholar

[12]

J. Stat. Phys., 151 (2013), 549-566. doi: 10.1007/s10955-012-0653-0.  Google Scholar

[13]

The Quarterly Journal of Economics, 106 (1991), 1039-1061. doi: 10.2307/2937956.  Google Scholar

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