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Mixed behavior network equilibria and quasi-variational inequalities
In the modeling of competition on networks it is usually assumed
that users either behave following the Wardropian user equilibrium or the
system optimum concept. Nevertheless, in several equilibrium
situations, for instance in urban traffic flows, intercity freight
flows and telecommunication networks, a mixed behavior is observed.
This paper presents a time-dependent network-based model shared by two
types of users: generalized Nash players and
user equilibrium players. Generalized Nash players have a significant impact on
the load of the network, whereas user equilibrium players have a negligible
impact. Both classes of players choose the paths to send their flows so
as to minimize their own costs, but they apply different optimization
criteria. Players interact via some implicit balance constraints
which depend on the equilibrium
solution. Thus, the equilibrium distribution is proved to be equivalent to the solution
of a time-dependent quasi-variational inequality problem.
Results on existence of solutions are discussed as well as a numerical example.