City logistics is a complex system of multiple agents (supply chains), independently optimizing their operations and making multiple decisions also affecting the other logistics agents and the society, playing a key economic role as well as generating externalities. A known policy is the introduction of an Urban Consolidation Center (UCC), which although has been shown to be environmentally beneficial, it often proved not economically sustainable. In the current work we consider a “single-site” UCC serving a confined urban area, e.g. a shopping mall. To better understand the economic impact of urban consolidation we model a N-to-one logistics network (multiple origins supplying one destination) in which the agents independently decide whether or not to entrust the UCC with their deliveries. We formulate an agent’s costs as functions of the other agents’ decisions in a twofold way: (i) by a congestion cost at destination that increases when more agents decide to deliver directly, (ii) by an increase of efficiency at the leg between the UCC and the destination when more agents choose to deliver through the UCC. We model the trade-off between congestion and network effects with a game with N symmetric players. We identify two stable Nash equilibria: one in which agents always deliver directly and one where the UCC has a positive demand. We prove that the planner, pursuing the social optimum, always favors a larger number of agents to consolidate, compared to the outcomes of the game. Finally, with numerical examples we compute the inefficiency generated by the game, motivating the introduction of subsidies or taxes by the planner.