Cellular Automata and Small-World as Enabling Technologies in Marketing Research

rucksackbulgeAI and Robotics

Dec 1, 2013 (3 years and 10 months ago)

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Cellular Automata and Small
-
World as
Enabling Technologies in Marketing Research


Jacob Goldenberg, Barak Libai, and Eitan Muller

Doctoral Consortium, Marketing Science Conference,

Erasmus University

Relevant material can be downloaded from:
www.complexmarkets.com

Q: How can we tie individual level behavior to
aggregate level data when individual behavior
depends on the action of others?


For example: where word
-
of
-
mouth and imitation strongly influence
behavior


An analytical analysis of such situations is not trivial


A: we turn to “adaptive complex system methods”
that allow us to simulative the (often simple)
behaviors of interconnected individuals and
examine the (often complex) aggregate results

Cellular Automata
and
Small World
are two such methods


Widely used in disciplines such as Physics, Biology &
Geography


Making its way into Sociology, Economics, Management and
Marketing

Watch Out! Forest Fires!*


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Each cell can take a finite number of states


The state of a cell in time t+1 depends on
the state of its neighbors in time t ,
according to some
transition rule


Time is advancing in discrete steps



In a
stochastic cellular automata

the
transition rule is stochastic

*The term “
wall of fire
” should be replaced with “
fingers of fire


Small
-
World environment is typically described as
a circle but can be described as a matrix as well



Each cell can take a finite number of states


The state of a cell in time t+1 depends on the state of its
neighbors in time t , according to some
transition rule


Time is advancing in discrete steps


The definition of “neighbors” change


instead of fixed
number of predetermined
strong ties

neighbors, some
random

weak
-
ties

acquaintances are added


Do they have to be random?

Running Cellular Automata for a number of periods


Enables the examination of the
global

consequences of a
certain set
individual level

parameters (e.g., local transition
rules or initial states )



Running the cellular automata with different individual level
parameters enables an “experiment” to analyze how a change
in these parameters influences global results

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-

a potential buyer

1
-

an adopter

p



the one period probability to adopt due to
external effects

q

-

the one period probability to adopt due to an
interaction with one adopter

Individual single period Probability of Adoption =
PA =1
-

(1
-
p)(1
-
q)
k

A marketing example:

Using Cellular Automata to examine the evolution of
markets for new products

Method: micro simulations

period 0

micro simulations

period 1

micro simulations

period 2

micro simulations

period 3

micro simulations

period 4

micro simulations

period 5

micro simulations

period 6

Advantages of Cellular Automata and Small World


Few assumptions


Very
flexible

(e.g., different networks, multiple social systems,
effects of competition)


Enables
spatial

analysis


With current computer power, large scale experiments can be
conducted



Yet, a strong theoretical base in the individual level is essential !!

Examples of small
-
world & cellular automata
studies



a) Utilizing
spatial
analysis for an early forecast of new
product success


b)
The evolution of markets for products with
network
externalities


c) Are “
weak ties
” really strong ?


a) Utilizing spatial analysis for an early forecast
of new product success



Using small
-
world, it can be shown that the evolution of
successful innovations happens in
geographical clusters
. If a
product is not accepted by the market, a more uniform
geographical distribution is expected

Success

Failure


The method was later tested successfully on real new products


Using small
-
world we demonstrated the ability of
cross entropy

-

a measure of distance between distributions
-

to detect early
-
on
departure of market growth from a Uniform distribution and
hence a forecast for success

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Success
Failure
b) The evolution of markets for products with
network externalities



The effect of previous adopters on adoption was historically
attributed in innovation diffusion research to
word
-
of
-
mouth
.


Yet, for “
network goods
” previous adoption has a major effect on the
product’s utility and hence adoption (in addition to w
-
o
-
m)



Combining
collective action

threshold models with cellular
automata we could model a process in which the “utility effect”
is separated from that of of word
-
of
-
mouth.


Adopter’s communicated with adopters in their vicinity but their utility
was also influenced by the number of total adopters.


Using cellular automata we could show how network externalities,
direct and indirect, create a strong “
chilling effect
” on new
product growth; in which stages of the product lifecycle it is
mostly felt; and what marketers can do to mitigate such an effect

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wi thout external ities
wi th external ities
Cellular automata resultant aggregate diffusion
curves: with and without network externalities

c) Are “weak ties” really strong ?


Interpersonal communications can occur within an
individual’s own personal group (
strong ties
) and weaker
and less personal communications that an individual makes
with a wide set of other acquaintances and colleagues
(
weak ties
). Granovetter 1973



Marketing research in this area focused on the individual
level (e.g., Brown and Reingen 1987 ) and did not examine
the effect of the tie structure on the aggregate level.


Using a hybrid cellular automata


small world
we examined the effect of network structure on
aggregate diffusion


We found that
despite the relative inferiority of the weak
ties parameter in the model’s assumptions, their effect
approximates or exceeds that of strong ties, in all stages of
the product life cycle.



We could examine the effect of other parameters. For
example,
when personal networks are small, weak ties
were found to have a stronger impact on information
dissemination than strong ties.


Other work we did with small world and
cellular automata


Understanding the dual market (“chasm”) effect on adoption


Examining the robustness of aggregate diffusion models
assumptions


Examining the effect of negative word
-
of
-
mouth on diffusion


Analyzing effective pricing for hardware/software products

Please, do try it at home!*


Take the setting of Norton and Bass technological substitution paper



Model a cellular automata framework in which a potential consumer
can take one of three forms:

0


has not yet adopted either generations of the technology

1


adopted the first generation of the technology

2


adopted the second generation



Now check the effects of entry time of the second generation on the
net cash flow of the firm


*as of today, no laptop is known to be injured, maimed or otherwise hurt


by one of these experiments

Hartelijk Bedankt