The Profitable Tour Problem (PTP) belongs to the class of Vehicle Routing Problems with profits. In PTP, a vehicle, starting from a central depot, can visit a subset of the available customers, collecting a specific revenue whenever a customer is visited. The objective of the problem is the maximization of the net profit, i.e., the total collected revenue minus the total route cost. Most of the literature in this field considers only one decision maker. However, in several real-world routing applications, and in particular in the last-mile delivery, there are different involved agents with conflicting goals. If the decisions are made in a hierarchical order, this problem can be modeled with bilevel programming, with the PTP at the lower level.

In this paper, we consider a company, which acts as a ``leader'' and offers disjoint subsets of a given set of items to a set of independent drivers. At the lower level, each driver solves a PTP communicating to the company the items she accepts to serve. Both the company and the drivers aim at maximizing their net profit, which is calculated differently in the two levels. We further propose two bilevel formulations that model this interaction allowing the leader not only to anticipate the best followers' response, but also to find the optimal pricing scheme for each carrier. The value function reformulations of the bilevel models are considered and further reformulated by projecting out some of the lower-level variables. We find exact solutions to these models using a branch and cut approach, leveraging on an alternative reformulation of the lower-level problems.