On the sufficiency of unidirectional incentive compatibility in auctions

Kiho Yoon

arxiv: 2606.03051 · v1 · pith:26SRSSHGnew · submitted 2026-06-02 · 💰 econ.TH

On the sufficiency of unidirectional incentive compatibility in auctions

Kiho Yoon This is my paper

Pith reviewed 2026-06-28 07:50 UTC · model grok-4.3

classification 💰 econ.TH

keywords auction designincentive compatibilityrevenue maximizationmechanism designlinear programming dualitydiscrete types

0 comments

The pith

Optimal auction revenue is unchanged when bidders can only underbid rather than bid freely.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that the highest revenue an auction can generate when bidders are limited to reporting lower values than their true ones is the same as when they can report any value. This is shown in a discrete type model using linear programming duality. The result means that for revenue maximization, it suffices to ensure incentive compatibility only in one direction. This matters for simplifying the design of auctions with multiple bidders where checking all possible deviations is complex.

Core claim

We show that the optimal revenue when bidders can only underbid their true values cannot exceed the optimal revenue when bidders may freely underbid or overbid. Thus, unidirectional incentive compatibility is sufficient for full incentive compatibility for revenue maximization. The proof is through linear programming duality in a discrete model of bidder types and values, which also makes it possible to analyze the feasibility of allocation rules in multi-agent environments.

What carries the argument

Linear programming formulation of the revenue maximization problem and its dual, applied to allocation rules with restricted deviation directions.

If this is right

The optimal auction can be found by optimizing only over downward incentive constraints.
This equivalence holds in multi-agent discrete environments.
Feasibility of allocation rules becomes easier to analyze under the restricted deviations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach may allow for simpler algorithms in computational mechanism design.
Similar sufficiency results could be investigated in continuous type spaces with appropriate regularity conditions.
Extensions to non-quasilinear settings would require separate analysis.

Load-bearing premise

Bidder types and values form a discrete set, enabling the linear programming approach to establish the equivalence.

What would settle it

An example with continuous bidder types where the revenue-maximizing auction under only underbidding yields strictly less revenue than under full incentive compatibility.

read the original abstract

We study optimal auction design when the direction of bidders' deviations is restricted. We show that the optimal revenue when bidders can only underbid their true values cannot exceed the optimal revenue when bidders may freely underbid or overbid. Thus, unidirectional incentive compatibility is sufficient for full incentive compatibility for revenue maximization. We prove this equivalence through linear programming duality in a discrete model, which makes it possible to analyze the feasibility of allocation rules in multi-agent environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Paper proves that unidirectional IC suffices for revenue-optimal auctions in discrete finite-type settings via a clean LP duality argument.

read the letter

The main thing to know is that in a discrete model with finite bidder types, the optimal revenue under unidirectional incentive compatibility (only underbidding allowed) equals the optimum under full IC. The proof exhibits equality between the two primal LPs by showing their duals imply the weaker constraint set cannot improve the objective.

The paper does this straightforwardly. It formulates the revenue-maximization programs, notes that unidirectional IC relaxes the constraints, and applies standard duality to bound the value. This is a precise technical clarification rather than a routine extension, and the discrete setting lets them state allocation feasibility exactly.

The result is scoped explicitly to quasilinear utilities and finite types, so there is no overclaim about continuous spaces. The argument contains no circularity or fitting to prior estimates.

A minor limitation is the lack of worked examples showing how existing auctions change under this equivalence, but that is not required for the core claim. The math and citation pattern look solid for what is attempted.

This is useful for mechanism-design researchers who set up auction LPs and want to drop redundant constraints. It is not field-reorganizing but a reliable simplification. I would bring it to a reading group focused on auction theory and would send it to peer review.

Referee Report

0 major / 2 minor

Summary. The paper claims that, in a discrete finite model of bidder types and values, the optimal revenue achievable under unidirectional incentive compatibility (bidders may only underbid their true values) equals the optimal revenue under full incentive compatibility (bidders may underbid or overbid). The equivalence is established by exhibiting equality between the corresponding primal revenue LPs via duality, which also permits analysis of allocation-rule feasibility in multi-agent settings.

Significance. If the result holds, it establishes that unidirectional IC suffices for revenue maximization in discrete type spaces, thereby simplifying mechanism design without loss of optimality. The manuscript earns credit for a self-contained LP-duality argument that is independent of fitted parameters or prior reductions and is explicitly scoped to finite discrete types.

minor comments (2)

[Abstract] The abstract and introduction could state the finite discrete type-space restriction more prominently in the opening sentence to prevent readers from extrapolating to continuous types.
Notation for the primal and dual programs (e.g., variables for allocations and payments) should be introduced once with a single consistent symbol set rather than re-defined across sections.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and recommendation to accept the manuscript. The report accurately captures the contribution of the LP-duality argument establishing equivalence between unidirectional and full incentive compatibility for revenue maximization in finite discrete type spaces.

Circularity Check

0 steps flagged

Derivation self-contained via LP duality; no circularity

full rationale

The paper proves equivalence of optimal revenue under unidirectional vs. full IC by exhibiting equality of the corresponding LPs (and their duals) in a finite discrete type space. The argument compares feasible sets and uses standard duality to bound the unidirectional optimum by the full-IC optimum; it contains no fitted parameters renamed as predictions, no self-citations as load-bearing premises, and no self-definitional steps. The result is scoped explicitly to the discrete quasilinear case and does not import uniqueness theorems or ansatzes from prior work by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no free parameters, invented entities, or detailed axioms visible beyond the stated discrete model.

axioms (1)

domain assumption Bidders have discrete, finite types and values.
Explicitly stated as the setting for the LP duality argument.

pith-pipeline@v0.9.1-grok · 5580 in / 982 out tokens · 18946 ms · 2026-06-28T07:50:38.669547+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Optimal Auctions for Constrained Buyers
cs.GT 2026-06 unverdicted novelty 7.0

In constrained multi-unit auctions, Myerson-style mechanisms are optimal for revenue-aligned objectives while buyer constraints enable strictly better outcomes for consumer-aligned objectives.

Reference graph

Works this paper leans on

6 extracted references · cited by 1 Pith paper

[1]

Mechanism design with weaker incentive compatibility constraints,

Celik, G. (2006), “Mechanism design with weaker incentive compatibility constraints,” Games and Economic Behavior56, 37-44

2006
[2]

Partially veriﬁable information and mechanism design,

Green, J., Laﬀont, J.-J. (1986), “Partially veriﬁable information and mechanism design,” Review of Economic Studies53, 447-456. 17

1986
[3]

Optimal procurement mechanisms for divisible goods with capacitated suppliers,

Iyengar, G., Kumar, A. (2008), “Optimal procurement mechanisms for divisible goods with capacitated suppliers,”Review of Economic Design12, 129-154. Kr¨ ahmer, D., Strausz, R. (2025), “Unidirectional incentive compatibility,”Journal of Eco- nomic Theory228, 106051

2008
[4]

An optimal auction for capacity constrained bidders: a network perspective,

Malakhov, A., Vohra, R. (2009), “An optimal auction for capacity constrained bidders: a network perspective,”Economic Theory39, 113-128

2009
[5]

Optimal auction design,

Myerson, R. (1981), “Optimal auction design,”Mathematics of Operations Research6, 58-73

1981
[6]

Global incentive constraints in auction design,

Moore, J. (1984), “Global incentive constraints in auction design,”Econometrica52, 1523– 1535. 18

1984

[1] [1]

Mechanism design with weaker incentive compatibility constraints,

Celik, G. (2006), “Mechanism design with weaker incentive compatibility constraints,” Games and Economic Behavior56, 37-44

2006

[2] [2]

Partially veriﬁable information and mechanism design,

Green, J., Laﬀont, J.-J. (1986), “Partially veriﬁable information and mechanism design,” Review of Economic Studies53, 447-456. 17

1986

[3] [3]

Optimal procurement mechanisms for divisible goods with capacitated suppliers,

Iyengar, G., Kumar, A. (2008), “Optimal procurement mechanisms for divisible goods with capacitated suppliers,”Review of Economic Design12, 129-154. Kr¨ ahmer, D., Strausz, R. (2025), “Unidirectional incentive compatibility,”Journal of Eco- nomic Theory228, 106051

2008

[4] [4]

An optimal auction for capacity constrained bidders: a network perspective,

Malakhov, A., Vohra, R. (2009), “An optimal auction for capacity constrained bidders: a network perspective,”Economic Theory39, 113-128

2009

[5] [5]

Optimal auction design,

Myerson, R. (1981), “Optimal auction design,”Mathematics of Operations Research6, 58-73

1981

[6] [6]

Global incentive constraints in auction design,

Moore, J. (1984), “Global incentive constraints in auction design,”Econometrica52, 1523– 1535. 18

1984