We study cost-sharing mechanisms for several fundamental NP-hard combinatorial optimization problems. A cost-sharing mechanism is a protocol that, given bids for a service, determines which bidders to serve and what prices to charge. The mechanism incurs a subset-dependent cost that is implicitly defined by an instance of a combinatorial optimization problem. Three desirable but mutually incomp...

The equitable division of a joint cost (or a jointly produced output) among agents with different shares or types of output (or input) commodities, is a central theme of the theory of cooperative games with transferable utility. Ever since Shapley’s seminal contribution in 1953, this question has generated some of the deepest axiomatic results of modern microeconomic theory. More recently, the ...

We study the best guarantees of efficiency approximation achievable by cost-sharing mechanisms. Our main result is the first quantitative lower bound that applies to all truthful cost-sharing mechanisms, including randomized mechanisms that are only truthful in expectation, and only β-budget-balanced in expectation. Our lower bound is optimal up to constant factors and applies even to the simpl...