Strategyproof sharing of submodular costs: budget balance versus efficiency

A service is produced for a set of agents. The service is binary, each agen t either receives service or not, and the total cost of service is a submod ular function of the set receiving service. We investigate strategyproof me chanisms that elicit individual willingness to pay, decide who is served, a nd then share the cost among them. If such a mechanism is budget balanced ( covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms and find that the mechanism associated with the Shapley value co st sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance - th e more common route in the literature - we find that there is a single Clar ke-Groves mechanism that satisfies certain reasonable conditions: we call t his the marginal cost pricing mechanism. We compare the size of the margina l cost pricing mechanism's worst budget surplus with the worst welfare loss of the Shapley value mechanism.