Equilibria for nonatomic routing games with heterogeneous players

Abstract

This paper considers a problem that describes a stable state of a congested network involving a large number of heterogeneous users. In a congested network, if there is no central authority that regulates the network flows, the behavior pattern of the network flows is best represented by a noncooperative game, and the Nash equilibrium becomes the key solution concept. This paper, by extension, introduces random coefficients to a disutility function of the game, in order to reflect the network users' heterogeneous preferences. The existence and uniqueness of equilibrium in games with these player-specific coefficients are to be examined. The existence is established by the Brouwer fixed point theorem. The result on the uniqueness extends earlier work by Milchtaich (2005), and shows the possibility that topological conditions for which a network has a unique equilibrium can be relaxed in the proposed games.