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Kinetic modeling of economic games with large number of participants
On a continuous mixed strategies model for evolutionary game theory
| 1. | Dipartimento di Scienze di Base e Applicate per l’Ingegneria (SBAI), Università degli Studi “Sapienza” di Roma, Italy |
| 2. | Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, c/o Dip. di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1; I-00133 Roma |
| 3. | Dipartimento di Matematica & CMCS, Università degli Studi di Ferrara, Italy |
References:
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I. Bomze, Dynamical aspects of evolutionary stability, Mon. Math., 110 (1990), 189-206.
doi: 10.1007/BF01301675. |
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D. Challet, M. Marsili and Y-C. Zhang, "Minority Games: Interacting Agents in Financial Markets," Oxford University Press, 2005. |
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R. Cressman, Stability of the replicator equation with continuous strategy space, Mathematical Social Sciences, 50 (2005), 127-147.
doi: 10.1016/j.mathsocsci.2005.03.001. |
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L. Desvillettes, P.-E. Jabin, S. Mischler and G. Raoul, On selection dynamics for continuous structured populations, Commun. Math. Sci., 6 (2008), 729-747. |
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D. Friedman, Towards evolutionary game models of financial markets, Quantitative Finance 1, (2001) |
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A. Galstyan, Continuous strategy replicator dynamics for multi-agent learning, arXiv:0904.4717v1. |
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S. Genieys, N. Bessonov and V. Volpert, Mathematical model of evolutionary branching, Mathematical and Computer Modelling, 49 (2009), 2109-2115.
doi: 10.1016/j.mcm.2008.07.018. |
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J. Henriksson, T. Lundh and B. Wennberg, A model of sympatric speciation through reinforcement, Kinet. Relat. Models, 3 (2010), 143-163.
doi: 10.3934/krm.2010.3.143. |
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J. Hofbauer, J. Oechssler and F. Riedel, Brown-von Neumann-Nash dynamics: The continuous strategy case, Games and Economic Behavior, 65 (2009), 406-429.
doi: 10.1016/j.geb.2008.03.006. |
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J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, 1998. |
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T. W. L. Norman, Dynamically stable sets in infinite strategy spaces, Games and Economic Behavior, 62 (2008), 610-627.
doi: 10.1016/j.geb.2007.05.005. |
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J. Oechssler and F. Riedel, Evolutionary dynamics on infinite strategy spaces, Econ. Theory, 17 (2001), 141-162.
doi: 10.1007/PL00004092. |
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M. Ruijgrok and T. W. Ruijgrok, Replicator dynamics with mutations for games with a continuous strategy space, arXiv:nlin/0505032v2. |
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J. W. Weibull, "Evolutionary Game Theory," MIT Press, Cambridge, MA, 1995. |
show all references
References:
| [1] |
P. Abrams, Modelling the adaptive dynamics of traits involved in inter- and intraspecific interactions: An assessment of three methods, Ecol. Lett., 4 (2001), 166-175.
doi: 10.1046/j.1461-0248.2001.00199.x. |
| [2] |
I. Bomze, Dynamical aspects of evolutionary stability, Mon. Math., 110 (1990), 189-206.
doi: 10.1007/BF01301675. |
| [3] |
D. Challet, M. Marsili and Y-C. Zhang, "Minority Games: Interacting Agents in Financial Markets," Oxford University Press, 2005. |
| [4] |
R. Cressman, Stability of the replicator equation with continuous strategy space, Mathematical Social Sciences, 50 (2005), 127-147.
doi: 10.1016/j.mathsocsci.2005.03.001. |
| [5] |
L. Desvillettes, P.-E. Jabin, S. Mischler and G. Raoul, On selection dynamics for continuous structured populations, Commun. Math. Sci., 6 (2008), 729-747. |
| [6] |
D. Friedman, Towards evolutionary game models of financial markets, Quantitative Finance 1, (2001) |
| [7] |
A. Galstyan, Continuous strategy replicator dynamics for multi-agent learning, arXiv:0904.4717v1. |
| [8] |
S. Genieys, N. Bessonov and V. Volpert, Mathematical model of evolutionary branching, Mathematical and Computer Modelling, 49 (2009), 2109-2115.
doi: 10.1016/j.mcm.2008.07.018. |
| [9] |
J. Henriksson, T. Lundh and B. Wennberg, A model of sympatric speciation through reinforcement, Kinet. Relat. Models, 3 (2010), 143-163.
doi: 10.3934/krm.2010.3.143. |
| [10] |
J. Hofbauer, J. Oechssler and F. Riedel, Brown-von Neumann-Nash dynamics: The continuous strategy case, Games and Economic Behavior, 65 (2009), 406-429.
doi: 10.1016/j.geb.2008.03.006. |
| [11] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, 1998. |
| [12] |
T. W. L. Norman, Dynamically stable sets in infinite strategy spaces, Games and Economic Behavior, 62 (2008), 610-627.
doi: 10.1016/j.geb.2007.05.005. |
| [13] |
J. Oechssler and F. Riedel, Evolutionary dynamics on infinite strategy spaces, Econ. Theory, 17 (2001), 141-162.
doi: 10.1007/PL00004092. |
| [14] |
M. Ruijgrok and T. W. Ruijgrok, Replicator dynamics with mutations for games with a continuous strategy space, arXiv:nlin/0505032v2. |
| [15] |
J. W. Weibull, "Evolutionary Game Theory," MIT Press, Cambridge, MA, 1995. |
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