In purpose of going deep into the quantitative relation between system optimism and user equilibrium，which are two classical methods of traffic assignment, the perspective of game theory is adopted. Through non-corporative game analysis to the example, it is showed that system optimism and user equilibrium can be integrated to pure strategy Nash equilibrium under infinite strategy sets. Exiting as two particular situations of Nash equilibrium, they can be converted to each other with change of the number of game players. Furthermore, the conversion process between system optimism and user equilibrium is analyzed, which is characterized by two different stages. As the number of players grows, the result of Nash equilibrium leaves away from system optimism for user equilibrium quite quickly, suggesting the inefficiency of management measures trying to achieve system optimism. The impact that parameters in impedance functions exert on process is also researched, and it is argued that the free flow travel time, which reflects the primary advantages of the route, has great influence on conversion speed and tendency.
Can Wang and Yu-qingTang REF measure the system optimism and user equilibrium in a system through the result of Nash equilibrium?.