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 (J Econ Theory 64:20-34, 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.