Network equilibrium with mixed behavior

The classical Wardropian principle hypothesize that users minimize either individual travel cost or overall system cost. In reality, users do not always behave in such a manner; instead, they are both competing and cooperating, typically when there exists oligopoly Cournot-Nash firms. In this paper, we formulate a mixed network equilibrium model as variational inequalities (VI) that simultaneously describe the routing behaviors of user equilibrium (UE), system optimum (SO) and Cournot-Nash (CN) players. Each player is presumed to make a routing decision given the knowledge of the routing strategies of the other players. After examining the existence and uniqueness of solutions, the diagonalization approach is applied to find a mixed equilibrium solution.