Cooperative Provision of Indivisible Public Goods

A community faces the obligation of providing an indivisible public good that each of its members is able to provide at a certain cost. The solution is to rely on the member who can provide the public good at the lowest cost, with a due compensation from the other members.This problem has been studied in a non-cooperative setting by Kleindorfer and Sertel (1994). They propose an auction mechanism that results in an interval of possible individual contributions whose lower bound is the equal division. Here, instead we take a cooperative stand point by modelling this problem as a cost sharing game that turns out to be a "reverse" airport game whose core is shown to have a regular structure. This enables an easy calculation of the nucleolus that happens to define the upper bound of the Kleindorfer-Sertel interval. The Shapley value instead is not an appropriate solution in this context because it may imply compensations to non-providers