A game-theoretic multi-stakeholder model for cost allocation in urban consolidation centres

Recently, many European local authorities have set up Urban Consolidation Centres (UCC) for dealing with challenges arising from the environmental and social impacts of logistical activities in urban contexts through shipment synchronisation and carrier coordination policies. However, the number of successful UCC projects led by local authorities in Europe is low, with most of the UCCs failing to achieve financial sustainability after the initial experimental phase, which is often heavily supported by public funds. In order to propose mechanisms that could favour the economic and financial sustainability of UCC systems, this research develops an adaptation of game-theoretic approaches to the problems of responsibility and cost allocation among stakeholders participating in a UCC delivery network. A solution based on the Shapley Value concept is employed to derive cost allocations; applications of the model to a real-world scenario are evaluated. An extensive sensitivity analysis shows that the proposed cost allocation rules can provide alternative arrangements, based on extended responsibility concepts, which can alleviate the burden on local authorities for the set up of UCCs. As such, results provide useful policy and practice implications on how to safeguard UCCs’ viability under different scenarios, including the outsourcing of the last-mile deliveries

Polluted river problems and games with a permission structure

When a polluted river passes through several different regions, a challenging question is how should the costs for cleaning the river be shared among the regions. Following Ni and Wang (2007) and Dong et al. (2012), we first show that the Upstream Equal Sharing method and the Downstream Equal Sharing method coincide with the conjunctive permission value (van den Brink and Gilles, 1996) of an associated game with a permission structure, which is obtained as the Shapley value of an associated restricted game. Two main advantages of this approach are (i) we obtain new axiomatizations of the two sharing methods based on axiomatizations of the conjunctive permission value, and (ii) by applying the alternative disjunctive permission value, obtained as the Shapley value of a different restricted game, we propose the new Upstream Limited Sharing method and provide an axiomatization