Sequential Pivotal Mechanisms for Public Project Problems

It is well-known that for several natural decision problems no budget balanced Groves mechanisms exist. This has motivated recent research on designing variants of feasible Groves mechanisms (termed as ‘redistribution of VCG (Vickrey-Clarke-Groves) payments’) that generate reduced deficit. With this in mind, we study sequential pivotal mechanisms and consider optimal strategies that can lower the taxes that the players would have to pay under the simultaneous mechanism. We show that for various variants of public project problems such strategies do exist. These strategies differ from truth-telling. In particular, we exhibit an optimal strategy with the property that a maximal social welfare is generated when each player follows it. Finally, we show that this improvement over the pivotal mechanism is achieved by an implementation in Nash equilibrium that is also Pareto optimal.