Efficient cost sharing with a cheap residual claimant

For the cooperative production problem where the commons is a one dimensional convex cost function, I propose the residual mechanism to implement the efficient production level . In contrast to the familiar cost sharing methods such as serial, average and incremental, the residual mechanism may subsidize an agent with a null demand. IFor a large class of smooth cost functions, the residual mechanism generates a budget surplus that is, even in the worst case, vanishes as 1/logn where n is the number of participants. Compare with the serial, average and incremental mechanisms, of which the budget surplus, in the worst case, converges to the efficient surplus as n grows. The second problem is the assignment among n agents of p identical objects and cash transfers to compensate the losers. We assume p<n, and compute the optimal competitive performance among all VCG mechanisms generating no budget deficit. It goes to zero exponentially fast in n if the number of objects is fixed; and as (n)^(1/2) uniformly in p. The mechanism generates envy, and net utilities are not co-monotonic to valuations. When p>n/2, it may even fail to achieve voluntary participation.