A model of interaction of travelers, parking agency and authorities for optimization free and paid parking

The system of two parking lots is researched: paid and free. The task of the city authorities is to determine part of the land for parking agency. The agency selects the best parking fee, and travelers determine which parking to choose. The goals of each participant are different: passengers attempt to minimize the loss of time and parking fees, the agency maximizes profits, and the city thinks about the public good (in this case, about all travelers). The mutual dependence of participants leads to the need to apply game theory to describe their interaction. The mathematical model defines restrictions on the parameters for existence Nash equilibrium. The numerical example that does not contradict the existing picture of the world is considered.