Sequential pivotal mechanisms for public project problems

TL;DR

This paper explores sequential pivotal mechanisms in public project problems, demonstrating strategies that reduce deficits, maximize social welfare, and are implementable in Nash equilibrium, advancing the design of efficient, budget-balanced mechanisms.

Contribution

It introduces optimal strategies for sequential pivotal mechanisms that reduce deficits and maximize social welfare, with proven Nash equilibrium implementation.

Findings

Existence of strategies reducing deficit in sequential pivotal mechanisms

Strategies lead to maximal social welfare when followed by all players

Strategies are implementable in Nash equilibrium

Abstract

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 mechanisms and consider optimal strategies that could reduce the deficit resulting under the simultaneous mechanism. We show that such strategies exist for the sequential pivotal mechanism of the well-known public project problem. We also exhibit an optimal strategy with the property that a maximal social welfare is generated when each player follows it. Finally, we show that these strategies can be achieved by an implementation in Nash equilibrium.