A note on toll competition on private roads: To lead or not to lead?

Toll competition between to private operators who wish to maximise their own profit is either modelled as a Nash game leading to lower profits than could be obtained in a collusive optimum or as a Stackelberg game whereby one operator is assumed to lead the process and anticipate the response of the follower. In previous examples it has been shown that the leader may be worse off than the follower. In this paper we examine the conditions under which one or both of the operators prefers to lead and conversely when they prefer to follow. We vary the capacities and free flow times of the two roads and find that when free flow times are equal there is no capacity combination where either player prefers to lead. Even when a player has an advantage in free flow time the region where this player prefers to lead is limited. Finally we look at the welfare implications of the results and find that where society would prefer one player to lead, that player prefers to follow.