Paradoxes may occur when different traffic equilibrium models are applied starting from the same data. When in the traffic system “players” of different size are present, a Mixed Behavior Equilibrium can be stated. One should expect, by intuition, that total cost decreases with the reduction of noncooperative players on the network. This assumption does not hold in general. This paper provides numerical examples to show it. The problem of investigating the relationship between different equilibrium models arises when one considers a strategy for rerouting vehicles in road networks, in order to reduce congestion (Route Guidance Systems, for example). The importance of identifying paradoxical situations in such problems is briefly discussed.