Welfare Undominated Groves Mechanisms

TL;DR

This paper introduces a measure to compare Groves mechanisms based on the welfare they generate, characterizes welfare undominated mechanisms in specific domains, and analyzes their optimality and limitations.

Contribution

It defines welfare undominated Groves mechanisms and characterizes them for auctions with identical units and public project problems, extending understanding of optimal mechanism design.

Findings

Welfare undominated mechanisms are characterized for anonymous linear payment functions.

The family of optimal-in-expectation linear redistribution mechanisms is welfare undominated in certain auction settings.

The VCG mechanism is welfare undominated in public project problems with equal costs, but not in more general cases.

Abstract

A common objective in mechanism design is to choose the outcome (for example, allocation of resources) that maximizes the sum of the agents' valuations, without introducing incentives for agents to misreport their preferences. The class of Groves mechanisms achieves this; however, these mechanisms require the agents to make payments, thereby reducing the agents' total welfare. In this paper we introduce a measure for comparing two mechanisms with respect to the final welfare they generate. This measure induces a partial order on mechanisms and we study the question of finding minimal elements with respect to this partial order. In particular, we say a non-deficit Groves mechanism is welfare undominated if there exists no other non-deficit Groves mechanism that always has a smaller or equal sum of payments. We focus on two domains: (i) auctions with multiple identical units and unit-demand bidders, and (ii) mechanisms for public project problems. In the first domain we analytically characterize all welfare undominated Groves mechanisms that are anonymous and have linear payment functions, by showing that the family of optimal-in-expectation linear redistribution mechanisms, which were introduced in [6] and include the Bailey-Cavallo mechanism [1,2], coincides with the family of welfare undominated Groves mechanisms that are anonymous and linear in the setting we study. In the second domain we show that the classic VCG (Clarke) mechanism is welfare undominated for the class of public project problems with equal participation costs, but is not undominated for a more general class.