Strictly strategy-proof auctions

TL;DR

This paper characterizes strictly strategy-proof mechanisms in one-dimensional private value settings, showing they are equivalent to strict monotonicity plus the envelope formula, and can be achieved with minimal modifications.

Contribution

It provides a new characterization of strict strategy-proofness, demonstrating its equivalence to strict monotonicity plus the envelope formula, and shows it can be implemented with negligible changes.

Findings

Strict strategy-proofness is equivalent to strict monotonicity plus the envelope formula.

Strategy-proofness can be made strict with arbitrarily small modifications.

Strictness in strategy-proof mechanisms is essentially free to achieve.

Abstract

A strictly strategy-proof mechanism is one that asks agents to use strictly dominant strategies. In the canonical one-dimensional mechanism design setting with private values, we show that strict strategy-proofness is equivalent to strict monotonicity plus the envelope formula, echoing a well-known characterisation of (weak) strategy-proofness. A consequence is that strategy-proofness can be made strict by an arbitrarily small modification, so that strictness is 'essentially for free'.