the rise and fall of fads and fashion - anamaria berea william … · 2017-02-16 · the rise and...

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


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


America’s Next Top Model

Modeling Fashion - From Runway Model to Network Model



From Visually Appealing Fashion to Visually AppealingModels - In Manhattan

Figure 1 : Visualization of Spatial Movement of Designers in Manhattan



From Visually Appealing Fashion to Visually AppealingModels - On Campus

Figure 2 : Visualization of Fashion Colors in Cambridge, MA



From Visually Appealing Fashion to Visually AppealingModels - The Social Media Influencers

Figure 3 : A New World for Trendsetting 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



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)



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



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)



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



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



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.




0 200 400 600 800 1000

-2e+29

-1e+29

0e+00

1e+29

2e+29

Index

Num

ber o

f Ado

pter

s


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.




0 200 400 600 800 1000

02

46

810

Index

Num

ber o

f Ado

pter

s


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.



Boundary Conditions for Parameters

NO,NIA,NIB ⊆ NNO,NIA,NIB < Nmax , where Nmax is a finite number.αO , αI , βI , βO , π ∈ [0, 1]




0 200 400 600 800 1000

02

46

810

Index

Num

ber o

f Ado

pter

s



Figure 8 : Behavior of Fashion Diffusion with Parametric Boundaries.




0 200 400 600 800 1000

0100

200

300

400

Index

Num

ber o

f Ado

pter

s







0 200 400 600 800 1000

02

46

8

Index

Num

ber o

f Ado

pter

s






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


An Agent-Based Model of Fashions and Fads

ABM Setup

Demo:

Figure 11 : Behavior of Fashion Diffusion Analytical vs. Simulation.



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


Figure 12 : Behavior of Fashion Diffusion Analytical vs. Simulation.



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



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.



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.



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.


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



Future Work

statistical significance of results

empirical validation

spatial modeling



Questions?

Thank You!

the rise and fall of fads and fashion - anamaria berea william … · 2017-02-16 · the rise and...

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