the rise and fall of fads and fashion - anamaria berea william … · 2017-02-16 · the rise and...
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The Rise and Fall of Fads and Fashion
The Rise and Fall of Fads and FashionAnamaria Berea
William RandRoland T. Rust
Center for Complexity in BusinessRobert H. Smith School of Business
University of Maryland
The Rise and Fall of Fads and Fashion
Table of Contents
1 America’s Next Top Model
2 An Analytical Model of Fashions and Fads
3 An Agent-Based Model of Fashions and Fads
4 Results and Conclusions
The Rise and Fall of Fads and Fashion
America’s Next Top Model
Modeling Fashion - From Runway Model to Network Model
The Rise and Fall of Fads and Fashion
America’s Next Top Model
From Visually Appealing Fashion to Visually AppealingModels - In Manhattan
Figure 1 : Visualization of Spatial Movement of Designers in Manhattan
The Rise and Fall of Fads and Fashion
America’s Next Top Model
From Visually Appealing Fashion to Visually AppealingModels - On Campus
Figure 2 : Visualization of Fashion Colors in Cambridge, MA
The Rise and Fall of Fads and Fashion
America’s Next Top Model
From Visually Appealing Fashion to Visually AppealingModels - The Social Media Influencers
Figure 3 : A New World for Trendsetting Fashion
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
From Visualizations to BehaviorTheoretical Premises and Conceptualization
Fashion diffuses from an Ingroup to an Outgroup(layers of trendsetters and adopters)
Figure 4 : The Ingroups – Outgroup Relationship
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Preference Heterogeneity in Trendsetting and Adoption
Ingroup a priori heterogeneity
one fraction of Ingroup only prefers Ingroup fashion(innovators)the other fraction of Ingroup prefers Ingroup fashion, but alsopays attention to Outgroup (both innovators and imitators)
Outgroup always prefers Ingroup fashion (imitators)
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Model Setup
preference parameters: αO , αI , βI , βO
heterogeneity parameter (Ingroup fraction of imitators/innovators):π
original sizes of the groups: NO, NIA, NIB
NO(t + 1) = αO ∗ (NIA(t) + NIB(t)) + βO ∗ NO(t)NIB(t + 1) = αI ∗ (1− π) ∗ (NIA(t) + NIB(t))− βO ∗ NO(t)NIA(t + 1) = αI ∗ π ∗ (NIA(t) + NIB(t))where NIA + NIB + NO = the whole market
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Results
Any of the groups behavior can be re-written as the followingsecond order difference equation:
f (t + 2) = (αI + βO)f (t + 1)− (αIβO + αOβI )f (t)
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
General Behavior of the Adoption Curves
The adoption curves can be re-written as:N(t) = c1x
t1 + c2x
t2 where
x1,2 are the solutions of the characteristic equationx2 − (αI + βO)x + (αIβO + αOβI ) = 0 andc1,2 = f (N(t0),N(t1)) – the initial group size for each group andthe size after one time step
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Group Sizes at t=0 and t=1
NO(t0) = NONIA(t0) = NIANIB(t0) = NIB
NO(t1) = αO(NIA + NIB) + βONONIA(t1) = αIπ(NIA + NIB)NIB(t1) = αI (1− π)(NIA + NIB)− βINO
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Behaviors
0 200 400 600 800 1000
-50
510
Index
Num
ber o
f Ado
pter
s
Ingroup AIngroup BOutgroup
AlphaI = 0.6 BetaI = 0.7 AlphaO= 0.8 BetaO= 0.7
Ni= 4 No= 10
Figure 5 : First Type of Oscillating Behavior of Fashion Diffusion.
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Behaviors
0 200 400 600 800 1000
-2e+29
-1e+29
0e+00
1e+29
2e+29
Index
Num
ber o
f Ado
pter
s
Ingroup AIngroup BOutgroup
alphaO= 1 alphaI= 0.2 betaO= 0.7 betaI= 1 p= 0.7 Outgroup= 5 IngroupA= 2 IngroupB= 10
Figure 6 : Second Type of Oscillating Behavior of Fashion Diffusion.
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Behaviors
0 200 400 600 800 1000
02
46
810
Index
Num
ber o
f Ado
pter
s
Ingroup AIngroup BOutgroup
alphaO= 0.1 alphaI= 0.8 betaO= 0.6 betaI= 0.1 p= 0.8 Outgroup= 2 IngroupA= 10 IngroupB= 6
Figure 7 : Third Type of Behavior of Fashion Diffusion.
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Boundary Conditions for Parameters
NO,NIA,NIB ⊆ NNO,NIA,NIB < Nmax , where Nmax is a finite number.αO , αI , βI , βO , π ∈ [0, 1]
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Behaviors
0 200 400 600 800 1000
02
46
810
Index
Num
ber o
f Ado
pter
s
Ingroup AIngroup BOutgroup
alphaO= 0.9 alphaI= 0.7 betaO= 0.1 betaI= 0.7 p= 0.3 Outgroup= 5 IngroupA= 10 IngroupB= 5
Figure 8 : Behavior of Fashion Diffusion with Parametric Boundaries.
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Behaviors
0 200 400 600 800 1000
0100
200
300
400
Index
Num
ber o
f Ado
pter
s
Ingroup AIngroup BOutgroup
alphaO= 0.9 alphaI= 0.6 betaO= 0.8 betaI= 0.6 p= 0.7 Outgroup= 4 IngroupA= 7 IngroupB= 7
Figure 9 : Behavior of Fashion Diffusion with Parametric Boundaries.
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Behaviors
0 200 400 600 800 1000
02
46
8
Index
Num
ber o
f Ado
pter
s
Ingroup AIngroup BOutgroup
alphaO= 0.3 alphaI= 0.6 betaO= 0.4 betaI= 0.1 p= 0.9 Outgroup= 9 IngroupA= 1 IngroupB= 3
Figure 10 : Behavior of Fashion Diffusion with Parametric Boundaries.
The Rise and Fall of Fads and Fashion
An Analytical Model of Fashions and Fads
Analytical Model Findings
The shape of the adoption curves for any of the groups is sensitiveto:
all the preference parameters: αO , αI , βI , βO
the initial sizes of the groups: NO, NIA, NIB
adoption can only be oscillatory with decreasing amplitude,oscillatory with increasing amplitude or decreasing to 0
The shape of the adoption curves for any of the groups is notsensitive to:
heterogeneity after time step t = 1
The Rise and Fall of Fads and Fashion
An Agent-Based Model of Fashions and Fads
ABM Setup
Demo:
Figure 11 : Behavior of Fashion Diffusion Analytical vs. Simulation.
The Rise and Fall of Fads and Fashion
An Agent-Based Model of Fashions and Fads
Dynamic Model
The no-network environment replication of the analytical model:
0 20 40 60 80 100
020
4060
80
Index
Num
ber o
f Ado
pter
s
alphaO= 0.9 alphaI= 0.1 betaO= 0.8 betaI= 0.1 p= 0.9 Outgroup= 7 IngroupA= 8 IngroupB= 1
Figure 12 : Behavior of Fashion Diffusion Analytical vs. Simulation.
The Rise and Fall of Fads and Fashion
An Agent-Based Model of Fashions and Fads
No-Network Environment Results
The high sensitivity to the initial conditions is being preserved.
(a) π = 0.5, alphaO = 0.6,βO = 0.7, NO = 10 (default)
(b) π = 0.4, alphaO = 0.6,βO = 0.7, NO = 10
(c) π = 0.6, alphaO = 0.6,βO = 0.7, NO = 10
(d) π = 0.5, alphaO = 0.3,βO = 0.7, NO = 10
(e) π = 0.5, alphaO = 0.6,βO = 0.6, NO = 10
(f) π = 0.5, alphaO = 0.6,βO = 0.7, NO = 7
The Rise and Fall of Fads and Fashion
An Agent-Based Model of Fashions and Fads
Network Model
Extension to the network environment - basic network topologies:
(a) random (b) preferential (c) small worlds
Figure 14 : The Network Environments in the ABM.
The Rise and Fall of Fads and Fashion
An Agent-Based Model of Fashions and Fads
Model Results
Extension to the network environment(controlling for the same set of parameters - i.e. π = 0.5, alphaO = 0.6,βO = 0.7, NO = 10):
(a) random (b) preferential (c) small worlds
Figure 15 : Model Behavior Under Different Network Topologies.
The Rise and Fall of Fads and Fashion
An Agent-Based Model of Fashions and Fads
Model Setup
Extension to the network environment(same parameters as above, but different network densities):
(a) dr = 0.1% (b) dp = 0.1% (c) ds = 3%
(d) dr = 9% (e) dp = 8.14% (f) ds = 8.26%
Figure 16 : Adoption Sensitivity to Network Density.
The Rise and Fall of Fads and Fashion
Results and Conclusions
Preliminary Results
explorations of the extension of analytical modeling withagent based/network modeling
analytical modeling shows high sensitivity to initial conditionsand low sensitivity to heterogeneity
network modeling shows sensitivity to network topology andnetwork density
The Rise and Fall of Fads and Fashion
Results and Conclusions
Future Work
statistical significance of results
empirical validation
spatial modeling
The Rise and Fall of Fads and Fashion
Results and Conclusions
Questions?
Thank You!