Jean-Michelle Dalle Model [1] shows the interactions among a finite number of agents on a toric network. Therefore, each agent interacts with its neighbors on the north, east, south, and west; and since it is a toric network, the agent on the top north interacts with the agent on the south-west corner of the agent as its north neighbor, top-east agent as its west neighbor and so on… In other words, on up to a 30×30 matrix, agent 1 on the first cell interacts with agents 2 [east], 11 [south], 10 [west], 91[north], etc…

There are two competing technologies, namely (1) and (-1), and represented with yellow and green respectively. Agents choose one of them randomly while being placed onto the matrix; then, based on the calculation at each step. Those calculations also take a parameter (b) – representing homogeneity – into account and calculate the probabilities for S of choosing technology (1) or (-1).

In this model, α represents the technology (1) or (-1), and probabilities are calculated according to this formula, whereas (b) [0<b<1] represents the heterogeneity/homogeneity of the technologies. The results give the probability for an agent (S) of choosing technology α.

Dalle states that in that kind of model, depending on the value of the parameter (b), there could be some technologies surviving at the niches; up to a critical value of (b). However, there exists a critical value bc, such that if b<bc, both technologies coexist in on average equal proportions, and if b>bc, there are two possible states where only one technology dominates, i.e., where standardization obtains. (Theorem 3; p.404).

Thus, the program runs ‘n’ times (the default is 5) for the parameter (b) for the value of b1 (the default is 0.001), and then the initial setting on the matrix is arranged once more, the parameter b increased (to 0.002 by default), and the program is re-run for another value of b until b reaches to 0.9.

Dalle also suggests that standardization always occurs if there is a global interaction apart from local interaction. In order to show that, Dalle gets a global agent, which is neighbor to all agents on the matrix, and the technology adopted by this agent is also taken into account (p.410).

Thus, the program gets the values for the neighbors at North (N), East (E), South (S) and West (W). Sums the values for the technologies adopted. In cases where Global Interaction is chosen, the program sets a fifth ‘neighbor’ who has chosen technology (1). It adds this into the calculation as the fifth member, as described in Dalle (p.410).

This simulation program is written using MS Visual Basic 6.0. In this program, a graphical user interface (GUI) is provided to set the parameters, such as;

- size of the grid (thus the number of the agents);
- value of the parameter (b);
- number of times that the simulation will run for each value of (b);
- if there would be global interactions.

In order to read the documentation about the program, click on the following link:

1 Dalle, JM., “Heterogeneity vs. externalities in technological competition: A tale of possible technological landscapes”, J EvolEcon (1997) 7: 395-41