Welfare maximization in stable sharing services

We propose a model of sharing of public services among local governments. Our model is an application of Nicoló et al. (2023) and combines features of two models: assignment games (Shapley and Shubik, 1971) and the division problem (Sprumont, 1991). I show that the SAM algorithm provided in Nicoló et al. (2023) generates a stable allocation that maximizes utilitarian welfare when preferences are Euclidean single-peaked. We then discuss the incentive compatibility of the solution proposed and the relation with welfare functions different from the utilitarian one.