Reinforcement-driven spread of innovations and fads

We investigate how social reinforcement drives the spread of permanent innovations and transient fads. We account for social reinforcement by endowing each individual with M + 1 possible awareness states 0, 1, 2,..., M, with state M corresponding to adopting an innovation. An individual with awareness k 1. When individuals can abandon the innovation at rate λ, the population fraction that remains clueless about the fad undergoes a phase transition at a critical rate λc; this transition is second order for M = 1 and first order for M > 1, with macroscopic fluctuations accompanying the latter. The time for the fad to disappear has an intriguing non-monotonic dependence on λ.

[1]  Daniel P Maki,et al.  Mathematical models and applications , 1973 .

[2]  S N Majumdar,et al.  Dynamics of efficiency: a simple model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M. Macy,et al.  The Emperor’s Dilemma: A Computational Model of Self‐Enforcing Norms1 , 2005, American Journal of Sociology.

[4]  Amy Jocelyn Glass,et al.  Product Cycles and Market Penetration , 1997 .

[5]  Frank M. Bass,et al.  Equilibrium Stochastic Choice and Market Penetration Theories: Derivations and Comparisons , 1976 .

[6]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[7]  David P. Myatt,et al.  Innovation Diffusion in Heterogeneous Populations: Contagion, Social Influence, and Social Learning , 2009 .

[8]  A. Astrov.  On world politics , 2005 .

[9]  A. Baronchelli,et al.  Consensus and ordering in language dynamics , 2009, 0901.3844.

[10]  S. Redner,et al.  A Kinetic View of Statistical Physics , 2010 .

[11]  Jukka-Pekka Onnela,et al.  Spontaneous emergence of social influence in online systems , 2009, Proceedings of the National Academy of Sciences.

[12]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[13]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[14]  J. M. Oshorn.  Proc. Nat. Acad. Sei , 1978 .

[15]  R Lambiotte,et al.  Role of second trials in cascades of information over networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[17]  J. Coleman,et al.  The Diffusion of an Innovation Among Physicians , 1957 .

[18]  B. Hayes.  Rumours and Errours , 2006 .

[19]  E. Rogers,et al.  Diffusion of innovations , 1964, Encyclopedia of Sport Management.

[20]  Spain,et al.  Cascade Dynamics of Complex Propagation , 2005, physics/0504165.

[21]  Brian Karrer,et al.  Message passing approach for general epidemic models. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Luca Dall'Asta,et al.  Effective surface-tension in the noise-reduced voter model , 2006, cond-mat/0612186.

[23]  Damon Centola,et al.  The Spread of Behavior in an Online Social Network Experiment , 2010, Science.

[24]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[25]  S. Lohmann.  The Dynamics of Informational Cascades: The Monday Demonstrations in Leipzig, East Germany, 1989–91 , 1994, World Politics.

[26]  P. Giles,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[27]  E Ben-Naim,et al.  Size of outbreaks near the epidemic threshold. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  F. Bass.  The Relationship between Diffusion Rates, Experience Curves, and Demand Elasticities for Consumer Durable Technological Innovations , 1980 .

[29]  Joachim Kaldasch,et al.  Evolutionary model of an anonymous consumer durable market , 2011 .

[30]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[31]  C. Gilligan,et al.  Synergy in spreading processes: from exploitative to explorative foraging strategies. , 2011, Physical review letters.