Strategyproof Sharing of Submodular Costs: Budget Balance versus Eeciency Stimulating Conversations With

A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be eecient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms; they correspond to the family of cost sharing formulae where an agent's cost share does not increase when the set of users expands. The mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require eeciency rather than budget balance { the more common route in the literature { we nd that there is a single Clarke-Groves mechanism that satisses certain reasonable conditions. This mechanism, which we call the marginal cost pricing mechanism, is vulnerable to manipulation by coalitions, and also may not fully cover costs (but never runs a budget surplus). We compare the size of the marginal cost pricing mechanism's worst budget surplus with the worst welfare loss of the Shapley value mechanism.

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