The petrol station game: the regional average price. A mean field analysis

In January 2023, the obligation for petrol stations to display the average fuel price calculated on a regional basis was introduced by the Italian Government. A mean field game model is here proposed to describe the evolution of the fuel price. In particular, each petrol station decides its own price, for the next day, taking account of an estimate of the average price, to be communicated by the Local Authority. The existence and the evolution of a mean field equilibrium are analytically investigated. Some simulations are compared with real data from the Autonomous Province of Trento, Italy.