Nash equilibrium in allocating space for paid and free parking, taking into account the interests of motorists, city authorities, and parking owners

Abstract

The problem of optimizаtion the distribution of urban territory near a center of gravity (airport, railway station, mall, etc.) between two types of parking lots: paid and free is considered. Obviously, under otherwise equal conditions the car user will choose free parking, but this will lead to an increase in the time to find a parking space. Therefore, paying for parking is beneficial for people who have a higher their value of time. Paid parking operator determine the size of the parking fee - if the price is low enough, all parking spaces will be occupied and there will be problems with parking, in addition, there will be lost profits. Lost profits will also occur if the price is high enough, because if the price goes up, fewer car users will be ready to use paid parking services. The city authorities' task is to determine part of the land which should be allocated for paid parking on the understanding that the rest of the land goes to free parking. The paid parking owners' task is to determine the optimal price in order to maximize the profit. Car users choose parking based on their value of time. A mathematical model was built with three types of participants: car users, municipal authorities and parking operators. The strategy of the passenger is the choice of parking, the goal is to minimize the cost and time. The strategy of the municipality is the allocation of territory for parking, the goal is similar to the goals of passengers. Parking operator with the strategy "parking price" achieves to maximize profit. The interaction of the participants is described within the framework of game theory, the objective functions of the players are considered, and the existence of the Nash equilibrium is proved. Numerical examples are considered, options for the development of the presented model are described. The dependence of characteristics on the total allocated number of parking spaces in two types of parking lots, the price of parking and the intensity of the car flow to the center of gravity is presented.