Efficient cost sharing with a cheap residual claimant

1 The residual claimant approach The residual claimant is a simple way to align monetary incentives and efficiency. Its most familiar application is to the rich class of Vicrey-Clarke-Groves (VCG) mechanisms. If individual preferences are quasi-linear in money (or any other numeraire) a VCG mechanism takes the "efficient" decision, except for the fact that the budget imbalance must be covered by a residual claimant ([?, 7]). Thus we achieve full efficiency (Pareto optimality) in the augmented economy where the claimant's preferences are taken into account, and he only cares about cash transfers. In this case we speak of residual efficiency in the initial economy. I submit that the realism of the residual claimant idea hinges around the size of the cash transfer he or she receives. If the residual claimant (thereafter RC) pockets a surplus commensurate to-or larger than-that available in the economy, the cost of generating the efficient decision is prohibitive: the RC receives a significant rent, and the choice of the entity playing the role of RC is a matter of dispute. These difficulties are amplified if the RC must finance a substantial deficit, in effect paying out an additional rent to the participants: now it may not even be feasible to find an entity willing to play the RC role. I propose a canonical mechanism, called residual * , to run a one commodity convex technology, and argue that its residual claimant is cheap for many specifications of the technology. The residual * mechanism is simpler than a VCG mechanism: individual messages are one-dimensional "demands", namely a request for a certain amount of output, which the mechanism must meet. Its incentives properties are weaker: individual demands are typically not dominant strategies. However for any profile of convex quasi-linear preferences, the non cooperative analysis of the demand game is quite straightforward, because it is a potential game ([15]). Even when information on preferences is entirely private, most familiar learning algorithms such as fictitious play and best reply dynamics converge to a Nash * This is an extended abstract of my paper "Efficient and almost budget-balanced cost sharing", available at