More and more people order products online and have parcels delivered to their homes. This leads to more congestion, negatively impacting the environment, public health, and safety. Carriers can use parcel lockers to consolidate and serve their customers to reduce these negative impacts. The implementation of a locker network can, however, be financially challenging. To overcome this, carriers can decide to collaborate and invest in parcel lockers together. In this paper, we introduce a stylized model in which a group of carriers can decide to position parcel lockers collectively. In this model, opening a locker comes at a cost, while serving a customer via close-by lockers generates a customer-specific profit. We introduce and study the associated cooperative game to investigate whether carriers can allocate the joint profit in a stable way. We prove that a stable allocation always exists for a particular class of networks. Generating a large set of instances, we introduce three possible allocation rules, and conduct several numerical experiments, showing that stable profit allocations are possible in most situations.