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**Jacob Goldenberg, Barak Libai, and Eitan Muller**

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:

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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

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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

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**Watch Out! Forest Fires!***

Each cell can take a finite number of states Time is advancing in discrete steps The state of a cell in time t+1 depends on the state of its neighbors in time t , according to some transition rule In a stochastic cellular automata the transition rule is stochastic *The term “wall of fire” should be replaced with “fingers of fire”

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**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 Time is advancing in discrete steps The state of a cell in time t+1 depends on the state of its neighbors in time t , according to some transition rule 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?

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**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 marketing example: Using Cellular Automata to examine the evolution of markets for new products**

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 0 - a potential buyer 1 - an adopter Individual single period Probability of Adoption = PA =1- (1-p)(1-q)k

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**Method: micro simulations period 0**

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**micro simulations period 1**

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**micro simulations period 2**

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**micro simulations period 3**

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**micro simulations period 4**

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**micro simulations period 5**

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**micro simulations period 6**

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**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 !!

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**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 ?

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**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

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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 The method was later tested successfully on real new products

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**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.

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**Cellular automata resultant aggregate diffusion curves: with and without network externalities**

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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**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.

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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.

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**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

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**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

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Hartelijk Bedankt

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