Budget-Balanced and Nearly Efficient Randomized Mechanisms: Public Goods and beyond

Many scenarios where participants hold private information require payments to encourage truthful revelation. Some of these scenarios have no natural residual claimant who would absorb the budget surplus or cover the deficit. Faltings [7] proposed the idea of excluding one agent uniformly at random and making him the residual claimant. Based on this idea, we propose two classes of public good mechanisms and derive optimal ones within each class: Faltings' mechanism is optimal in one of the classes. We then move on to general mechanism design settings, where we prove guarantees on the social welfare achieved by Faltings' mechanism. Finally, we analyze a modification of the mechanism where budget balance is achieved without designating any agent as the residual claimant.