Using Excel
Cellular automata and small-world models consist of three components:
- A graph representing individuals' adoption. In classical small- world models the world is usually (but not necessarily) drawn as a circle.
- Relationships among neighboring individuals. In small-world framework the weak relationships among non-neighboring individuals are to be specified as well.
- Transition rules of the probabilities of adoption between periods.
While the analyses in our papers are based on a C++ programs, we found that cellular automata and small world models can be built using Excel spreadsheets. These spreadsheets can stimulate intuition and first impressions, and moreover, comprehensive analyses can be conducted using carefully constructed Excel spreadsheets. In small-world, the weak relations are added for some individuals. The number of such relations is a small percentage of the total number of links (3%-5% as rule of thumb).
Hybrid cellular automata / small-world example
This Excel-based hybrid program exemplifies a market in which each individual communicates with all of his or her immediate neighbors. In addition, the entire market is divided into "communities", where the strength of the word-of-mouth activities varies depending on whether the communications are within a community or between communities.
Dual-market cellular automata example
This Excel-based cellular automata program exemplifies a market with two sub-markets: an early market of technophile adopters, and a main market of functionality-seeking adopters. The dual-market phenomenon treats the early market adopters and main market adopters as sufficiently different to warrant differential marketing treatment as two separate markets.
Cellular automata and small-world
Using agent based modeling tools such as cellular automata or small-world, a "would-be world" can be created to uncover the simple interactions that can lead to what could be considered a complex behavior. The shared pattern of these phenomena is their non-linearity and their surprising outcomes, such as a sudden drop in the adoption rate followed by an unexpected recovery phase.
In this figure there are six “caves” of relatively isolated clusters of consumers (denoted as circles) that communicate among themselves frequently and with strong influence. For example, one of the groups, denoted as net 3, consists of six individuals who are fully connected, and their strong ties are denoted by bold lines. The connections between the isolated clusters are made through a set of weaker ties that are denoted as dotted lines. These weak ties might change from one period to the next.
