Robust Market Design with Opaque Announcements

TL;DR

This paper explores the challenges of designing robust market mechanisms when the allocation process is announced opaquely, revealing that strategy-proofness cannot be guaranteed, but some other properties can.

Contribution

It introduces a framework for opaque announcements in market design and establishes fundamental impossibility and possibility results under opacity.

Findings

Strategy-proofness cannot be guaranteed under opacity.

Weak Maskin monotonicity can be achieved with opaque announcements.

Non-bossiness can be guaranteed under certain conditions.

Abstract

We introduce a framework where the announcements of a clearinghouse about the allocation process are opaque in the sense that there can be more than one outcome compatible with a realization of type reports. We ask whether desirable properties can be ensured under opacity in a robust sense. A property can be guaranteed under an opaque announcement if every mechanism compatible with it satisfies the property. We find an impossibility result: strategy-proofness cannot be guaranteed under any level of opacity. In contrast, in some environments, weak Maskin monotonicity and non-bossiness can be guaranteed under opacity.