The agents occupy the nodes of a square lattice (the grid). At each time step the agents update their posterior distribution of utilities according to their prior and the information they receive from their neighbors. They buy the brand that maximize their expected utility. Pollution dynamics occurs in parallel, the Laplacian operator being discretized by the standard method.
We used two kinds of initial distributions of agents:
-One can start from initial conditions where the grid is divided in two regions, an upper half plan where all agents have chosen polluting cars and a lower half plan where all agents have chosen non-polluting cars (see fig.2, 3 and 4). The gradient at the boundary between the two regions is maximum. In the range of parameters we use, we expect any change in the agent choices to start close to this boundary.
-In the other cases, see figures 6 and 7, we start from random distributions of polluters and non-polluters.
We monitor the configurations of purchases on the grid and the time evolutions of market shares and local pollution. The simulations are run iteratively until some attractor is reached. Examples of attractors are all agents choosing polluting cars or all agents choosing non-polluting cars.