Using the Theory of Games to Modelling the Equipment and Prices of Car Parking

Abstract

In large cities there are two serious problems connected with increasing number of cars. The first problem is the congestion of vehicles’ movement. The second one is too small of car parks, especially in centres of the cities. Authorities of cities and management of municipal streets introduce limitations in vehicles’ movement and reduce the number of car parks to minimalize streets crowd. That acting seems logical, but this is only the one point of view. From the other point of view municipal governments should aim to improve the level of the occupants’ life and assure the financial incomes, which enable to cover indispensable expenses. From this point of view, the municipal car parks are needed and bringing the profits element of municipal infrastructure. Cracow, which is one of the largest cities in Poland (about 760 thousands of occupants, and Cracovian agglomeration is about 1.4 million persons), was chosen as the object of the investigations. The zone of paid parking in Cracow, administered by the company belonging to city, has possessed 28837 parking places in 28.01.2016. In the zone there are assigned car parks or parking places near to the curbs and on pavements. The zone operates from Monday to Friday, from 10.00 to 20.00. Assuming using car parks only in 50% and fare of about 0.7 euro per hour, we receive incomes figuring out about 740000 euro/month. The purpose of the investigations was the identification of technical parameters of car parks being preferred by drivers. The investigations had been executed by method of questionnaires. Next the mathematical model of competition was made. The model was executed basing on the theory of games. Strategies of “Player 1” were prices and technical equipment of car parks and parking places lying in the zone of paid parking, administered by municipal company. Strategies of “Player 2” were prices and technical equipment of car parks belonging to private owners and two commercial centres in the city center. There were assumed that from the city’s point of view it is one rival, independently on the actual ownership of private car parks on whose strategy of acting the city do not have an influence. It is consistent with the basic foundations of the game theory. Both players compete for consumers - drivers using car parks, with such parameters like: price, distance from the destination, car parks’ equipment. The built model allows to indicate the best strategy. Knowing that strategy, one can form prices and equipment of car parks. That model may be used by municipal governments and companies which administer car parks. However, one should remember about limitations, which occur in reality, e.g. law restrictions referring to maximum prices for parking. The increasing pressure of cities’ authorities in Poland for changing those regulations, and examples of such solutions received, e.g. in USA, which concern varying prices for parking according to the demand on different car parks, and different hours, permit to have hopes, that the proposed model will be possible to use practically, soon.