Equilibria for Joint Congestion Game With Destination and Route Choices

We extend congestion games to the setting where players need to make multiple joint choices with interactions in a hierarchical manner (termed joint congestion game). At each choice dimension, players are involved in a typical congestion game. This game has a feature that the output of one choice dimension serves as an input of another one, and the costs paid by players in different choice dimensions are interdependent. Focusing on the joint congestion game with destination and route choices (i.e., select which destination and which route to complete a trip), we show the existence and uniqueness of the Nash equilibrium under mild assumptions in a nonatomic game setting. Then we investigate the property of the general quantal response equilibrium (QRE) for the joint congestion game in which players have perception errors of their costs (characterized by a probabilistic distribution). The QRE condition for the joint congestion game is further extended to the case where the analyst has only incomplete information about players’ perceived costs. A specific cross moment QRE model using the mean and covariance information is accordingly developed to account for both the analyst’s and players’ imperfect information/perception. We present an equivalent convex program that promises a unique solution for the cross moment QRE model, and provide a polynomial algorithm to solve it. Numerical results illustrate the features of the developed model for the joint congestion game and demonstrate the efficiency of the solution algorithm on two realistic transportation networks.