Potts Model - Diffusion of Innovations

For the last 6 months, I have been studying the diffusion of durable innovations using an adaptation of the Potts Model, a mathematical model originally used in physics to study the behavior of ferro-magnets. This model has been adapted to study a great variety of subjects, due to its attractive mathematical formulation; in this case, we can see adoption curves for two products and modify parameters to simulate different situations.

Each person is represented by a unique agent who starts off as a potential consumer. Each agent will eventually choose between consuming product A or product B, depending on the product’s attractiveness. This attractiveness is unique for each agent, and it depends on a combination of the product’s objective advantages and the consumption pattern of the agent’s neighbors. In this way, we try to simulate the behavior of an average consumer for an innovation, where the adoption of peers is usually very important because it plays an active role in the first two stages of the innovation-decision process described by Everett Rogers: Knowledge and Persuasion.

Moreover, the model has the possibility of defining “influence areas”, zones in the map where consumers are more likely to buy one or the other product, simulating geographic convenience that could arise for certain innovations.

Agent connections are a crucial element in this model, as they define the communication channels in the network, which affect the diffusion rate of the innovations. The user can decide between different reconnection probabilities, ranging from 0 (connections are strictly distance based, to the 8 nearest neighbors) to 0.16 (many random connections between agents), using small-world concepts from Watts and Strogatz.

A version of the model can be found and tried out here:

http://www.runthemodel.com/models/446/.

Enjoy!