Study On Models And Algorithms Of Urban Transit System Based On Game Theory

Based on the holistic analysis to urban public traffic system, the complicated interactions among the three classes of players in the urban public traffic system are discussed with the theory of games and optimizations in this dissertation. Besides the individual characters, the interactions among individuals are also considered. That is the magnificent difference from the other studies. The main contents of this dissertation are summarized as follows:(1) Against the traffic congestion that result form the insufficient use of vehicle and network, the urban public traffic system is portrayed as a special commodity market where passenger is consumer, transit operator is producer and the special goods is the service for passenger's trip. Firstly, a generalized Nash equilibrium game model is presented to describe how passengers adjust their route choices and trip modes. Secondly, the market equilibrium model for urban public traffic system is described as a series of mathematical programmings and equations, which is to reflect both the competitions among different transit operators and the interactive influences among passengers. Moreover, the proposed model can predict how passengers choose their optimal routes and trip modes simultaneously. And then, the algorithm is designed to obtain the equilibrium solution. Finally, a simple numerical example is given and some conclusions are drawn too.(2) Unlike the pure Wardropian equilibrium, in fact, there might be both competition and cooperation among travelers in urban traffic system, especially when there exists oligopoly Cournot-Nash firms. And because of the immense number of the travelers, we first classify the travelers into two classes, UE and CN. A mixed behavior network equilibrium model is formulated as a variational inequality that describes the routing behaviors of UE and CN players simultaneously. Then we present a Stackelberg game on the network in which the govern ment manager is the leader and the UE and CN players are the followers. The government manager tries to minimize the total system travel cost by adjusting the price. Using the marginal function approach, the Stackelberg game is formulated as an equivalent single-level optimization problem, where the lower level of variational inequality is represented by a differentiable gap function constraint. The augmented Lagrange penalty function method is used to solve the single-level optimization problem. The feasibility conclusion of method is presented and and a numerical example is shown at last.(3) After analyzing the competitive and cooperative relations among the urban public traffic operators, a generalized Nash equilibrium game model is presented. Considering the role of government manager, a Stackelberg game is brought forward to describe the dynamic adjustment process of the manager and players. The Stackelberg game of management is formulated as a mathematical program with equilibrium constraints (MPEC). We dispose this mathematical program problem with the similar method to the last model in this thesis. Using the gap function approach, the Stackelberg game is formulated as an equivalent single-level optimization problem, where the lower level of variational inequality is represented by a differentiable gap function constraint. The augmented Lagrange penalty function method is used to solve the single-level optimization problem. The feasibility of method is proved also.(4) A Cournot duopoly model is presented to describe the production competition between two operators in the urban public traffic market. The two monopolies will increase their productions by adding the number of vehicles or shortening the departing frequency to enhance their profits. But that is not the Pareto solution to the game though it is the Nash equilibrium. It is a typical Prisoner's Dilemma. How the prisoners to break away form the dilemma? After discussing the repeated game, it is found that if the game is repeated infinitely, the two monopoly operators must be willing to cooperate to get the Pareto solution.(5) With the wider attention and application of game theory, some serious questions are revealed. One of the questions is the ideal assuming of "full rational player". The real player, whatever individuals or a colletive, makes disicion always with some personal preferences and even makes mistakes unavoidably. In order to relax the rigorous full rationality condition to players, the bounded rationality factor is analyzed in the last Cournot duopoly model with revolutionary game. The Evolutionarily Stable Strategy(ESS) to this revolutionary game is presented and analyzed.