This model shows that agents with imperfect knowledge are able to switch to more expensive non-polluting devices by comparing information about pollution costs obtained from neighboring agents. When information sampling is local, the maximum accepted extra cost for the non-polluting device scales as the gradient of the pollution cost times the range of polling. Unless the pollution spatial distribution has very abrupt changes from maximum to minimum pollution (on distances lower than the range of polling), the accepted cost is less than the cost of pollution. Furthermore, except when the cost of the polluting device is very small with respect to sampled cost of pollution, the dynamics of invasion by the non-polluting devices is rather slow, much slower that the maximum velocity on the grid.
A surprising result of the simulations is the importance of the coexistence regions with regular patterns of cheaters and cooperators.
The memory range of the agents plays an important role in the dynamics of market domination: when a strong pollution gradient is established from the initial conditions, an intermediate memory range is optimum to favor the adoption of the non-polluting brand. In the presence of strong spatial (and thus temporal fluctuations), short term memories are an advantage allowing the agents to use the information generated by rapidly vanishing spatial fluctuations.
Another interesting result is the fact that invasion of the polluted region by the non-polluting devices does not always proceed from the non-polluted region. When mixed metastable attractors are reached, the polluted mixed region can be invaded from islets of non-polluting devices that started as fluctuations inside this region. Revolutions don't start in the most advanced countries, but rather in the most retrograde.
Some generalization are implemented simply in the present model. The role of constant taxes per polluting device imposed by a government simply decreases the prior utility of polluting devices. Changing the densities of agents between cities and country-side is also easily accomplished by having variable densities of agents on the grid.
We thank B. Derrida, F. Grau, V. Gremillion, A. Kirman, J.P. Nadal and J. Vannimenus for helpful discussions. SWARM software, thanks to Chris Langton and David Hiebeler, was used for numerical simulations. The Laboratoire de Physique Statistique is associated with (URA 1306 CNRS) ,Ecole Normale Supérieure, and universités Paris 6 et Paris 7 and we acknowledge financial support from NATO CRG 900998, Curie Foundation external grant program and the John D. and Catherine T. Mac Arthur Foundation, through the New Century Fund, the sponsor of Project 2050.
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