Fashion cycle dynamics induced by agents' heterogeneity for generic bell-shaped attractiveness functions

References

• M. Bianchi, Novelty, preferences, and fashion: When goods are unsettling, J. Econ. Behav. Organ. 47 (2002), pp. 1–18. doi: 10.1016/S0167-2681(01)00162-7
   Web of Science ®Google Scholar
• G.I. Bischi, U. Merlone, and E. Pruscini, Evolutionary dynamics in club goods binary games, J. Econ. Dyn. Control 91 (2018), pp. 104–119. doi: 10.1016/j.jedc.2018.02.005
   Web of Science ®Google Scholar
• A. Bisin and T. Verdier, The economics of cultural transmission and the dynamics of preferences, J. Econ. Theory 97 (2001), pp. 298–319. doi: 10.1006/jeth.2000.2678
   Web of Science ®Google Scholar
• L.S. Block and W.A. Coppel, Dynamics in One Dimension, Springer Lecture Notes 1513, Springer-Verlag, Berlin, 1992.
   Google Scholar
• L.E. Blume and D. Easley, Optimality and natural selection in markets, J. Econ. Theory 107 (2002), pp. 95–135. doi: 10.1006/jeth.2000.2764
   Web of Science ®Google Scholar
• W. Brian Arthur, Increasing Returns and Path Dependence in the Economy, University of Michigan Press, 1994.
   Google Scholar
• A. Cabrales and J. Sobel, On the limit points of discrete selection dynamics, J. Econ. Theory 57 (1992), pp. 407–419. doi: 10.1016/0022-0531(92)90043-H
   Web of Science ®Google Scholar
• J.P. Caulkins, R.F. Hartl, P.M. Kort, and G. Feichtinger, Explaining fashion cycles: Imitators chasing innovators in product space, J. Econ. Dyn. Control 31 (2007), pp. 1535–1556. doi: 10.1016/j.jedc.2006.05.008
   Web of Science ®Google Scholar
• F. Cavalli and A. Naimzada, A multiscale time model with piecewise constant argument for a boundedly rational monopolist, J. Differ. Equ. Appl. 22 (2016), pp. 1480–1489. doi: 10.1080/10236198.2016.1202940
   Web of Science ®Google Scholar
• F. Cavalli, A. Naimzada, and M. Pireddu, Emergence of complex social behaviors from the canonical consumption model, Mind Soc. (2015), DOI:10.1007/s11299-015-0169-9.
   Google Scholar
• F. Cavalli, A. Naimzada, and M. Pireddu, A family of models for Schelling binary choices, Physica A444 (2016), pp. 276–296. doi: 10.1016/j.physa.2015.10.038
   Web of Science ®Google Scholar
• F. Cavalli, A. Naimzada, and M. Sodini, Oligopoly models with different learning and production time scales, submitted.
   Google Scholar
• J. Chang and R. Stauber, Evolution of preferences in an exchange economy, Econ. Lett. 103 (2009), pp. 131–134. doi: 10.1016/j.econlet.2009.03.013
   Web of Science ®Google Scholar
• P.R.P Coelho and J.E. McClure, Toward an economic theory of fashion, Econ. Inq. 31 (1993), pp. 595–608. doi: 10.1111/j.1465-7295.1993.tb00893.x
   Web of Science ®Google Scholar
• G. Corneo and O. Jeanne, Segmented communication and fashionable behavior, J. Econ. Behav. Organ. 39 (1999), pp. 371–385. doi: 10.1016/S0167-2681(99)00046-3
   Web of Science ®Google Scholar
• V. Di Giovinazzo and A. Naimzada, A model of fashion: Endogenous preferences in social interaction, Econ. Model. 47 (2015), pp. 12–17. doi: 10.1016/j.econmod.2014.12.029
   Web of Science ®Google Scholar
• P.A. Diamond, National debt in a neoclassical growth model, Am. Econ. Rev. 55 (1965), pp. 1126–1150.
   Web of Science ®Google Scholar
• P. Dindo, A tractable evolutionary model for the Minority Game with asymmetric payoffs. Physica A 355 (2005), pp. 110–118. doi: 10.1016/j.physa.2005.02.073
   Web of Science ®Google Scholar
• E. Ekaterinchuk, J. Jungeilges, T. Ryazanova, and I. Sushko, Dynamics of a minimal consumer network with uni-directional influence, J. Evol. Econ. 27 (2017), pp. 831–857. doi: 10.1007/s00191-017-0517-5
   Web of Science ®Google Scholar
• E. Ekaterinchuk, J. Jungeilges, T. Ryazanova, and I. Sushko, Dynamics of a minimal consumer network with bi-directional influence, Commun. Nonlinear Sci. Numer. Simul. 58 (2018), pp. 107–118. doi: 10.1016/j.cnsns.2017.04.007
   Web of Science ®Google Scholar
• P. Frijters, A model of fashions and status, Econ. Model. 15 (1998), pp. 501–517. doi: 10.1016/S0264-9993(98)00030-3
   Web of Science ®Google Scholar
• W. Gaertner, A dynamic model of interdependent consumer behavior, J. Econ. 34 (1974), pp. 327–344.
   Google Scholar
• W. Gaertner, Periodic and aperiodic consumer behavior, Appl. Math. Comput. 22 (1987), pp. 233–254.
   Web of Science ®Google Scholar
• W. Gaertner and J. Jungeilges, A non-linear model of interdependent consumer behaviour, Econ. Lett.27 (1988), pp. 145–150. doi: 10.1016/0165-1765(88)90087-0
   Web of Science ®Google Scholar
• W. Gaertner and J. Jungeilges, “Spindles” and coexisting attractors in a dynamic model of interdependent consumer behavior: A note, J. Econ. Behav. Organ. 21 (1993), pp. 223–231. doi: 10.1016/0167-2681(93)90049-U
   Web of Science ®Google Scholar
• W. Gaertner and J. Jungeilges, A model of interdependent consumer behavior: Nonlinear dynamics in R2, in Models and Measurement of Welfare and Inequality, W. Eichhorn, ed., Springer-Verlag, Berlin, 1994, pp. 940–962.
   Google Scholar
• L. Gardini, I. Sushko, and K. Matsuyama, 2D discontinuous piecewise linear map: Emergence of fashion cycles. Chaos 28 (2018).
   Google Scholar
• R.E. Haymond and E.S. Thomas, Busy Dogs: A class of iteration problems, J. Diff. Equ. Appl. (1996), DOI:10.1080/10236199608808059.
   Google Scholar
• A. Heifetz, C. Shannon, and Y. Spiegel, The dynamic evolution of preferences, Econ. Theory 32 (2007), pp. 251–286. doi: 10.1007/s00199-006-0121-7
   Web of Science ®Google Scholar
• A. Heifetz, C. Shannon, and Y. Spiegel, What to maximize if you must, J. Econ. Theory 133 (2007), pp. 31–57. doi: 10.1016/j.jet.2005.05.013
   Web of Science ®Google Scholar
• J. Hofbauer and J. Weibull, Evolutionary selection against dominated strategies, J. Econ. Theory 71 (1996), pp. 558–573. doi: 10.1006/jeth.1996.0133
   Web of Science ®Google Scholar
• J. Jungeilges and T. Ryazanova, Transitions in consumption behaviors in a peer-driven stochastic consumer network, submitted
   Google Scholar
• J. Jungeilges, T. Ryazanova, and A. Mitrofanova, Sensitivity analysis of consumption cycles. Chaos 28 (2018). DOI:10.1063/1.5024033.
   PubMed Web of Science ®Google Scholar
• E. Karni and D. Schmeidler, Fixed preferences and changing tastes, Am. Econ. Rev. 80 (1990), pp. 262–267.
   Web of Science ®Google Scholar
• K. Matsuyama, Custom versus fashion: Path-dependence and limit cycles in a random matching game, Working Paper in Economics, E-92-11, Hoover Institution; Northwestern University CMS-EMS DP # 1030, (1991).
   Google Scholar
• A. Naimzada and M. Pireddu, Chaotic social interaction via endogenous reactivity, J. Diff. Equ. Appl. (2014), DOI:10.1080/10236198.2014.903938.
   Google Scholar
• A. Naimzada and M. Pireddu, Endogenous evolution of heterogeneous consumers preferences: Multistability and coexistence between groups, Econ. Lett. 142 (2016), pp. 22–26. doi: 10.1016/j.econlet.2016.02.018
   Web of Science ®Google Scholar
• A. Naimzada and M. Pireddu, An evolutive discrete exchange economy model with heterogeneous preferences, Chaos Solit. Fract. 111 (2018), pp. 35–43. doi: 10.1016/j.chaos.2018.03.041
   Web of Science ®Google Scholar
• A. Naimzada and M. Pireddu, Complex dynamics in an evolutionary general equilibrium model, Discrete Dyn. Nat. Soc. 2018 (2018), Article ID 8471624, 13 pages. doi: 10.1155/2018/8471624
   Google Scholar
• A. Naimzada, and M. Pireddu, Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences. Chaos 28 (2018). DOI:10.1063/1.5024931.
   Web of Science ®Google Scholar
• A. Naimzada and M. Pireddu, Strong coexistence for a model with endogenous evolution of heterogeneous agents, Commun. Nonlinear Sci. Numer. Simul. 65 (2018), pp. 35–53. doi: 10.1016/j.cnsns.2018.05.006
   Web of Science ®Google Scholar
• W. Pesendorfer, Design innovation and fashion cycles, Am. Econ. Rev. 85 (1995), pp. 771–792.
   Web of Science ®Google Scholar
• W.H. Sandholm, Population Games and Evolutionary Dynamics, MIT Press, Cambridge, 2010.
   Google Scholar
• A.N. Sharkovsky, S.F. Kolyada, A.G. Sivak, and V.V. Fedorenko, Dynamics of One-Dimensional Maps, Kluwer Academic, Boston, 1997.
   Google Scholar
• G. Simmel, Fashion, Am. J. Sociol. 62 (1957), pp. 541–558. doi: 10.1086/222102
   Web of Science ®Google Scholar
• F. Vigneron and L. Johnson, A review and a conceptual framework of prestige-seeking consumer behavior, Acad. Mark. Sci. Rev. 3 (1999), pp. 1–15.
   Google Scholar
• S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Texts in Applied Mathematics, 2nd ed., Springer, New York, 2003.
   Google Scholar
• W.-B. Zhang, Fashion with snobs and bandwagoners in a three-type households and three-sector neoclassical growth model, Rev. Mex. Econ. Finan. 11 (2016), pp. 1–19.
   Google Scholar
• W.-B. Zhang, Fashion and business cycles with snobs and bandwagoners in a multi-sector growth model, J. Bus. 2 (2017), pp. 1–13. doi: 10.18533/job.v2i3.73
   Google Scholar