The general philosophy of agent based simulations such as this one, is to correlate observed dynamical regimes with the range of parameters where they are observed. The dynamical regimes are characterised by the attractor they reach. We have then searched the transition parameters separating in the parameter space the regions corresponding to different attractors, such as domination of the market by polluting or non-polluting cars.
We kept invariant the following parameters:
The 32x32 grid. We used circular boundary conditions: the upper row (resp. left colummn) of the grid is connected to the lower (resp. the right colummn).
Initial standard deviations
and
were set to 1.
The risk aversion parameter
was set to 5.
In most simulations, 5 neighbors were polled to obtain information. This number was sometimes changed to 12.
The pollution diffusion rate was set to 0.5 and the evaporation rate was 0.2.
At a given pollution cost, the most influential
parameter with respect to which attractor is reached
is the difference in prior utilities of both brands.
A priori utilities for polluting cars,
were set to 10.
A priori utilities for non-polluting cars,
,
were varied downward from 10. When
is close to
, the decrease in posterior utilities
due to pollution is sufficient to make the agents
prefer non-polluting cars. When the differences in prior
utilities is increased, some threshold is
reached were an inverse process is observed:
the region of non-polluting cars buyers is invaded by
polluting cars, and partial domination of polluting cars
is achieved. The agents don't agree any more
to pay for the extra cost of the catalytic converter.
The difference in prior
utilities at the threshold, represent
the maximum price that the agent
would agree to pay to avoid the pollution costs.
We have systematically searched these thresholds
for the above range of parameters:
was varied between 1 and 1024
which corresponds to memory decay times of 1 and 200.
Pollution rates were 5, 10 and 20, which correspond
to maximum pollution costs of 20, 40 and 80
(these values are slightly less
because
of time and space discretization on the grid).