Envy Freedom and Prior-free Mechanism Design

TL;DR

This paper develops a framework for prior-free mechanism design, introducing envy-free outcomes as benchmarks, and demonstrates that simple mechanisms can approximate optimal revenue without prior knowledge of agent distributions.

Contribution

It characterizes optimal envy-free outcomes in symmetric environments and shows that mechanisms approximating these outcomes perform well without prior distribution assumptions.

Findings

Envy-free outcomes can serve as benchmarks for prior-free mechanisms.

A generalized random sampling auction achieves constant approximation.

Envy-free mechanisms are structurally similar to incentive-compatible mechanisms.

Abstract

We consider the provision of an abstract service to single-dimensional agents. Our model includes position auctions, single-minded combinatorial auctions, and constrained matching markets. When the agents' values are drawn from a distribution, the Bayesian optimal mechanism is given by Myerson (1981) as a virtual-surplus optimizer. We develop a framework for prior-free mechanism design and analysis. A good mechanism in our framework approximates the optimal mechanism for the distribution if there is a distribution; moreover, when there is no distribution this mechanism still performs well. We define and characterize optimal envy-free outcomes in symmetric single-dimensional environments. Our characterization mirrors Myerson's theory. Furthermore, unlike in mechanism design where there is no point-wise optimal mechanism, there is always a point-wise optimal envy-free outcome. Envy-free outcomes and incentive-compatible mechanisms are similar in structure and performance. We therefore use the optimal envy-free revenue as a benchmark for measuring the performance of a prior-free mechanism. A good mechanism is one that approximates the envy free benchmark on any profile of agent values. We show that good mechanisms exist, and in particular, a natural generalization of the random sampling auction of Goldberg et al. (2001) is a constant approximation.