Abstract: The work presented is part of a collaboration between mathematicians and philosophers of ethics, politics, and society aiming to understand mechanisms of green energy transition where some kind of interaction between many subjects and collective behaviors seem to play a role. We have identified as a first example the case of solar photovoltaic, with the purpose of explaining the time series of Italy and of different regions. We use tools from continuous-time Markov chains, mean field limits, optimal control, and mean field games.

Then, we specify our analysis on the case of domestic installations. In order to explain them we propose a Markovian model of interacting particle systems to describe the decision of a significant proportion of the general public in Italy on the installation of solar photovoltaics (PVs) and compare our models to real data. We assume that the adoption decision follows a well precise pattern. First, the general public develops a certain level of sensitivity to climate change and environmental issues. Then it plans to install the PVs because she/he has a sufficient amount of information on the benefits of PVs. Finally, it installs PVs because the economic benefits out-weights the costs. In conclusion, we propose some original policies, not based not on financial incentives. This work is in collaboration with Franco Flandoli (SNS), Giulia Livieri (SNS), Silvia Morlacchi (SNS), Fausto Corvino (University of Gothenburg) and Alberto Pirni (SSSA).