Strategy-proof club formation with indivisible club facilities

We investigate the strategy-proof provision and financing of indivisible club good facilities when individuals are subject to congestion costs that are non-decreasing in the number of other club members and in a private type parameter. An allocation rule specifies how the individuals are to be partitioned into clubs and how the costs of the facilities are to be shared by club members as a function of the types. We show that some combinations of our axioms are incompatible when congestion costs are continuous and strictly increasing in the type parameter, but that all of them are compatible if congestion costs are dichotomous and there is equal cost sharing. We present a number of examples of allocation rules with equal cost sharing and determine which of our axioms they satisfy when the congestion cost is linear in the type parameter. We also show that using iterative voting on ascending size to determine a club partition is not, in general, strategy-proof when each facility's cost is shared equally.