مدل تئوری بازی ها شبکه های ترافیک شهری عمومی

We have studied urban public traffic networks from the viewpoint of complex networks and game theory. Firstly, we have empirically investigated an urban public traffic network in Beijing in 2003, and obtained its statistical properties. Then a simplified game theory model is proposed for simulating the evolution of the traffic network. The basic idea is that three network manipulators, passengers, an urban public traffic company, and a government traffic management agency, play games in a network evolution process. Each manipulator tries to build the traffic lines to magnify its “benefit”. Simulation results show a good qualitative agreement with the empirical results.

Complex networks can describe variety different practical systems [1], [2], [3], [4] and [5]. It may serve as a useful tool for understanding complex systems. One way to study complex networks may be performing empirical investigation first and then set up suitable models to understand the common dynamical characteristics and mechanism of the systems. Since urban public traffic systems are practically important, they have been extensively and intensively studied in recent years [6], [7], [8], [9], [10] and [11]. Among the studies, [6] suggests a network description for both the urban public traffic systems in Beijing and Yangzhou. Each bus line is defined as a “collaboration act” and each bus station as a node (“actor”). An edge is connected between a pair of bus stations if they take part in one bus line. We suggest, in this paper, that the urban public traffic company, the passengers and the government traffic management agency take most important roles on the urban public traffic network evolution. Each of the three manipulators competes with others to magnify its “benefit”. The urban public traffic company firstly considers its income benefit, the passengers may only consider their convenience and ticket expenses, and the government traffic management agency may consider the effectiveness and public safety. Meanwhile, they know that the game will be over if any of the three gives up, so they prepare to give in if any side cannot bear. This keeps the collaboration between them. The evolution process of the network may be described by such a process, in which the three manipulators play games, and finally it reaches an equilibrium, which leads to a situation where the network benefits all the three manipulators equally. Based on this idea, in this paper we suggest a simplified network evolution model. To our knowledge, this is the first discussion of a manipulator game in a network. This idea may be suitable for description of some other systems evolution. Section 2 presents the statistical properties of urban public traffic network in Beijing in 2003. Section 3 presents our model and its evolution. The simulation results are shown in Section 4. A summary and discussion are given in the last section.

We show that a simplified game theory model may simulate the evolution process of the urban public traffic network. To our knowledge, this is the first time a network manipulator game investigation has been suggested. Usually the network game investigation concerns some famous game models (e.g., the prisoner's dilemma or the snowdrift) and some famous network models (e.g., the small-world model or the scale-free model). The researches are important, however often have to discuss games between many nodes. We argue that in some systems games cannot be performed between nodes, and the evolution of the network is due to games between several network manipulators. This may lead to very simple and straightforward understanding. We believe that this idea is interesting, not just for the understanding of the traffic system, but also for many cooperation- competition systems.