Nonbossy Mechanisms: Mechanism Design Robust to Secondary Goals

TL;DR

This paper explores how mechanism design can be made robust to agents' hidden secondary goals by characterizing incentive-compatible and nonbossy mechanisms across various settings, revealing new mechanisms that outperform traditional ones.

Contribution

It provides a complete characterization of incentive-compatible and nonbossy mechanisms, introducing new mechanisms that outperform standard posted-price mechanisms in complex environments.

Findings

Sequential posted-price mechanisms are characterized as the only incentive-compatible, individually rational, nonbossy mechanisms in single-item settings.

In complex environments, mechanisms satisfying the characterization outperform posted-price mechanisms in revenue and efficiency.

Nonbossy mechanisms are essential for robustness against secondary goals in various mechanism design settings.

Abstract

We study mechanism design when agents may have hidden secondary goals which will manifest as non-trivial preferences among outcomes for which their primary utility is the same. We show that in such cases, a mechanism is robust against strategic manipulation if and only if it is not only incentive-compatible, but also nonbossy -- a well-studied property in the context of matching and allocation mechanisms. We give complete characterizations of incentive-compatible and nonbossy mechanisms in various settings, including auctions with single-parameter agents and public decision settings where all agents share a common outcome. In particular, we show that in the single-item setting, a mechanism is incentive-compatible, individually rational, and nonbossy if and only if it is a sequential posted-price mechanism. In contrast, we show that in more general single-parameter environments, there exist mechanisms satisfying our characterization that significantly outperform sequential posted-price mechanisms in terms of revenue or efficiency (sometimes by an exponential factor).