An efficient and almost budget balanced cost sharing method

In the residual∗ cost sharing game with a convex technology, the equilibrium demands maximize total surplus, but total payment may differ from the actual cost, and a user with a null demand may be subsidized. If the cost function is totally monotone (e.g., polynomial with positive coefficients, or exponential), participation is voluntary and total payment covers actual cost. The ratio of excess payment to the efficient surplus is no larger than min{ 2 logn , 1}, where n is the number of potential users. For power cost functions, C(a) = ap, p > 1, the above ratio converges to zero as 1 np−1 . Participation appears to be voluntary however a small budget deficit is possible. For analytic cost functions, the ratio converges to zero exponentially when the set of users increases. All properties above are lost if the cost function is not smooth. ∗I am greatly indebted to Fedor Nazarov at Michigan State University, for the crucial insight into the proof of Theorem 1, and to Doug Hensley at Texas A&M, who provided numerical simulations in support of a key conjecture. I am also grateful to participants in the 2006 AGATE workshop in Bertinoro, and in the meetings of the Society for Economic Design in Bodrum. This work is supported by the NSF under grant SES-0414543.