Thursday, October 15, 2009

THE LINK BETWEEN POPULATION DYNAMICS AND VIRAL MARKETING


Arpan ghosh | IIM shillong

Introduction:
Can marketing be done in the same way that an epidemic spreads in a certain population? This paper is a set of ideas that I feel shows the relationship between the laws of the natural world and the business world. It seems that the extension of the Cournot’s Duopoly Model in economics from two to n competitive firms follows the same graphical representation as that of the population of a particular species living in a closed ecosystem. This would prompt the thought that the behavior of an organization (both the firms and the animal population being organizations with defined hierarchies) would remain essentially the same whatever be its surrounding in the sense that the Darwinian laws of competition and the survival of the fittest seem to apply. Now the question is can this hypothesis be extended to the social setting where a human population also has the same hierarchical structure albeit not as explicitly stated or properly defined as that of a school of fish or a colony of ants. This is where I believe that population dynamics will meet swarm theory. I believe that the overall size of the population in a closed ecosystem (population dynamics) will be affected by Darwin’s laws but how the existing population behaves at a particular moment can be mapped by swarm theory. The center of the population and its outline will define the entire population and this can be utilized by today’s modern marketers for their benefit.

Objective and Problem:
The idea that I am proposing in this paper has been worked upon before, but not in the same form. The concept of viral marketing involves spreading an idea in a certain target market through “word of mouth” .But this process, I believe , is unstructured and uncontrolled in the sense that the advertisers cannot be certain whether their message will reach the right people, cover the entire market or have the desired effect. Now what I want to do is to see if somehow, if I want to advertise (spread an idea), can I identify the centers of power (the people) that will be the most potent amplification points for the spread to the entire population?

People believe friends, family and acquaintances much more strongly and willingly than they do the typical salesman. That means that if I am targeting only the 10 most influential (in real not nominal terms) people from a population of 100 to carry my idea forward, I am in effect increasing both speed and brand equity while cutting costs drastically.

Methodology and hypothesis:
Now, again the question is - how does one identify the center(s) of a population. This problem will be compounded by the fact that the population size will keep changing during the period of determination, the individuals power to act as the center may vary and the biggest problem of them all- The search for the power points will have to be conducted from the boundaries towards the center of the population spread.

This is where chaos should play a part. As individuals are iteratively eliminated to get to the real center of power, a small miss in the initial assessment may ultimately lead to a completely different entity than what I was looking for and render the whole study useless. I believe that given a particular population, every individual/ organism should have a viral potential. We can plot these on a graph and then try to plot the “most critical path” (MCP)- a connection between all these high viral potential individuals. This will form the main conduit of information flow throughout the population. Any other communication or interaction with others in their sphere of influence is a bonus. The communication flow has to be along the MCP to allow the spread to the entire population in the most efficient manner. Other communication will result in redundancies. That means that we have to identify the “center” and then work outwards in order to find local solutions .When we reach the outer edge of the population we have to make a path from the center (global solution) through the local solutions.
Thus taking both methods together, I believe that this will be a 2 stage search in which we will first work outside- in, eliminating local solutions along the way in order to get to the global best fit according to the viral potential magnitude. Once this recursive elimination is over, we will have to work outwards again, picking the eliminated local maxima and studying their interaction effects with the non- solutions in order to determine whether they or the global solution have a higher influencing power on that point of the population.

The viral potential will solely be the influencing power of the solution in a positive manner in order to spread the company’s requirements in the fastest and least costly manner. This leads to the intuitive result that I can fiddle around with viral potential that is increase it with positive reinforcements or decrease it with negative ones. But here again economies of scale will kick in as increasing the reinforcements beyond a certain point will lead to decreasing results as the sphere or the level of influence cannot increase beyond a certain point.
We can define a parameter for the level of influence that a particular solution has on the surrounding points. As soon as the level of computed influence drops below the defined level, we have to look for a solution that better influences the points and thus optimize our agents for the maximum impact.

Global Optimization and Search Method:
One way to solve this problem is to do a search of the feasible solution set and look to optimize the solution. This would be a constraint bound programming where we would be maximizing the objective function. I believe that this should be a 2 stage search – the first to identify a global maximum that should be the starting point of the propagation. This type of search I believe has already been incorporated in memetic algorithms (MAs) or hybrid genetic algorithms. This will lead to a kind of a concentric search where the constraints will be used to obtain feasible solution sets in each iteration thereby evolving newer populations. This should ideally lead us to the starting point of propagation, the individual having the highest or lowest value of the objective function.

In another perspective for a more evolved search we can look at a meta- Lamarckian MA that have the candidate solutions competing based on incentives to generate local improvements. An improvement of this process will be a third generation MA that will have the constraints and the search parameters also evolving along with the progression of the search for feasible solutions.

Conclusion:
The idea for this approach is in a fledgling stage, but the benefit if an optimal search method can be developed will be huge. Any organization will be able to pinpoint the individuals it has to target to ensure that its product or idea is spread to each and every target in the population. Thus potentially, before the product launch in a country or region the entire market size, regional distribution and demographics can be estimated. The only limitation of the solution, if it is possible, at this juncture is the scalability of the model and the huge computations required for calculating the viral potentials and doing the global search.

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