Existence and efficiency of oligopoly equilibrium under toll and capacity competition

This paper studies the existence and efficiency of oligopoly equilibrium under simultaneous toll and capacity competition in a parallel-link network subject to congestion. We establish sufficient conditions for the existence of a pure-strategy oligopoly equilibrium and then derive upper bounds on the efficiency loss of the oligopoly equilibrium over the social optimum under different inverse demand function assumptions, respectively. Furthermore, we show that these bounds are demand-function free and only dependent upon the number of competitive roads.