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Cellular Automata and Small-World as Cellular Automata and Small-World as Enabling Technologies in Marketing Enabling Technologies in Marketing Research Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing Science Conference, Erasmus University Relevant material can be downloaded from:
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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.

Mar 26, 2015

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Page 1: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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

ResearchResearch Jacob Goldenberg, Barak Libai, and Eitan Muller

Doctoral Consortium, Marketing Science Conference, Erasmus University

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

Page 2: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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

Page 3: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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

Page 4: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

Watch Out! Forest Fires!*

1 0 1 1 1 1 1 0 0 1

0 0* 0 1 1 1 1 1 1 1

0 0 1 0 1 1 1 1 1 1

0 1 1 1 0 1 1 1 0 1

0 1 1 0 0 1 1 1 1 1

1 1 0 0 1 0 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

111 000 111 11 11 11 11 00 00 11

000 0*0* 000 11 11 11 11 11 11 11

000 000 111 00 11 11 11 11 11 11

00 11 11 11 00 11 11 11 00 11

00 11 11 00 00 11 11 11 11 11

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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”

Page 5: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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?

Page 6: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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

1 0 1 1 1 1 1 0 0 1

0 0* 0 1 1 1 1 1 1 1

0 0 1 0 1 1 1 1 1 1

0 1 1 1 0 1 1 1 0 1

0 1 1 0 0 1 1 1 1 1

1 1 0 0 1 0 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

111 000 111 11 11 11 11 00 00 11

000 0*0* 000 11 11 11 11 11 11 11

000 000 111 00 11 11 11 11 11 11

00 11 11 11 00 11 11 11 00 11

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Page 7: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

0 - 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

Page 8: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

Method: micro simulationsperiod 0

Page 9: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

micro simulationsperiod 1

Page 10: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

micro simulationsperiod 2

Page 11: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

micro simulationsperiod 3

Page 12: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

micro simulationsperiod 4

Page 13: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

micro simulationsperiod 5

Page 14: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

micro simulationsperiod 6

Page 15: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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 !!

Page 16: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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 ?

Page 17: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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

Page 18: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

• 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

Product 1

0

0.1

0.2

0.3

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0.6

1 2 3 4 5 6 7 8 9

product 2

0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6 7 8 9

product 3

0

0.1

0.2

0.3

0.4

0.5

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1 2 3 4 5 6 7 8 9

product 4

0

0.1

0.2

0.3

0.4

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1 2 3 4 5 6 7 8 9

Success

Failure

Page 19: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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.

Page 20: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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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without externalities with externalities

Cellular automata resultant aggregate diffusion curves: with and without network

externalities

Page 21: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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.

Page 22: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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.

Page 23: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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

Page 24: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

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 technology1 – adopted the first generation of the technology2 – 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

Page 25: Cellular Automata and Small-World as Enabling Technologies in Marketing Research Jacob Goldenberg, Barak Libai, and Eitan Muller Doctoral Consortium, Marketing.

Hartelijk BedanktHartelijk Bedankt