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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, United States |
References:
[1] |
T. Adriaansen, D. Armbruster, K. G. Kempf and H. Li, An agent model for the high-end gamers market, Advances in Complex Systems, 16 (2013), 1350028, 33pp.
doi: 10.1142/S0219525913500288. |
[2] |
D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains, SIAM J. Appl. Math, 66 (2006), 896-920.
doi: 10.1137/040604625. |
[3] |
F. M. Bass, A new product growth model for consumer durables, Mathematical Models in Marketing, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 351-253.
doi: 10.1007/978-3-642-51565-1_107. |
[4] |
L. Boltzmann, The second law of thermodynamics, Theoretical Physics and Philosophical Problems, Vienna Circle Collection, 5 (1974), 13-32.
doi: 10.1007/978-94-010-2091-6_2. |
[5] |
C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory Of Dilute Gases, Springer-Verlag, 1994.
doi: 10.1007/978-1-4419-8524-8. |
[6] |
P. Degond, J.-G. Liu and C. Ringhofer, Large-scale dynamics of mean-field games driven by local Nash equilibria, J. Nonlinear Sci., 24 (2014), 93-115.
doi: 10.1007/s00332-013-9185-2. |
[7] |
P. Degond, J.-G. Liu and C. Ringhofer, Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria, J. Stat. Phys., 154 (2014), 751-780.
doi: 10.1007/s10955-013-0888-4. |
[8] |
D. Helbing, A mathematical model for attitude formation by pair interactions, Behavioral sciences, 37 (1992), 190-214. |
[9] |
R. J. LeVeque, Finite Volume Methods For Hyperbolic Problems, Cambridge University Press, 2002.
doi: 10.1017/CBO9780511791253. |
[10] |
H. Li, D. Armbruster and K. G. Kempf, A population-growth model for multiple generations of technology products, Manufacturing & Service Operations Management, 15 (2013), 343-360.
doi: 10.1287/msom.2013.0430. |
[11] |
L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations And Monte Carlo Methods, Oxford University Press, 2014. |
[12] |
G. Toscani, C. Brugna and S. Demichelis, Kinetic models for the trading of goods, J. Stat. Phys., 151 (2013), 549-566.
doi: 10.1007/s10955-012-0653-0. |
[13] |
A. Tversky and D. Kahneman, Loss aversion in riskless choice: A reference-dependent model, The Quarterly Journal of Economics, 106 (1991), 1039-1061.
doi: 10.2307/2937956. |
show all references
References:
[1] |
T. Adriaansen, D. Armbruster, K. G. Kempf and H. Li, An agent model for the high-end gamers market, Advances in Complex Systems, 16 (2013), 1350028, 33pp.
doi: 10.1142/S0219525913500288. |
[2] |
D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains, SIAM J. Appl. Math, 66 (2006), 896-920.
doi: 10.1137/040604625. |
[3] |
F. M. Bass, A new product growth model for consumer durables, Mathematical Models in Marketing, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 351-253.
doi: 10.1007/978-3-642-51565-1_107. |
[4] |
L. Boltzmann, The second law of thermodynamics, Theoretical Physics and Philosophical Problems, Vienna Circle Collection, 5 (1974), 13-32.
doi: 10.1007/978-94-010-2091-6_2. |
[5] |
C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory Of Dilute Gases, Springer-Verlag, 1994.
doi: 10.1007/978-1-4419-8524-8. |
[6] |
P. Degond, J.-G. Liu and C. Ringhofer, Large-scale dynamics of mean-field games driven by local Nash equilibria, J. Nonlinear Sci., 24 (2014), 93-115.
doi: 10.1007/s00332-013-9185-2. |
[7] |
P. Degond, J.-G. Liu and C. Ringhofer, Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria, J. Stat. Phys., 154 (2014), 751-780.
doi: 10.1007/s10955-013-0888-4. |
[8] |
D. Helbing, A mathematical model for attitude formation by pair interactions, Behavioral sciences, 37 (1992), 190-214. |
[9] |
R. J. LeVeque, Finite Volume Methods For Hyperbolic Problems, Cambridge University Press, 2002.
doi: 10.1017/CBO9780511791253. |
[10] |
H. Li, D. Armbruster and K. G. Kempf, A population-growth model for multiple generations of technology products, Manufacturing & Service Operations Management, 15 (2013), 343-360.
doi: 10.1287/msom.2013.0430. |
[11] |
L. Pareschi and G. Toscani, Interacting Multiagent Systems: Kinetic Equations And Monte Carlo Methods, Oxford University Press, 2014. |
[12] |
G. Toscani, C. Brugna and S. Demichelis, Kinetic models for the trading of goods, J. Stat. Phys., 151 (2013), 549-566.
doi: 10.1007/s10955-012-0653-0. |
[13] |
A. Tversky and D. Kahneman, Loss aversion in riskless choice: A reference-dependent model, The Quarterly Journal of Economics, 106 (1991), 1039-1061.
doi: 10.2307/2937956. |
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