A non-cooperative game is formulated on a transportation network with congestion. The players are associated with origin-destination pairs, and are facing demand functions at their respective destination nodes.

A Nash-Cournot equilibrium is defined and conditions for existence and uniqueness of this solution are provided. The asymptotic behaviour of the Nash-Cournot equilibrium is then shown to yield (under appropriate assumptions) a total flow vector corresponding to a Wardrop equilibrium.