As Stated

Case record · Mechanism design

Safe implementation

Malachy J. Gavan and Antonio Penta · Theoretical Economics 20(4) (2025), 1285–1322 · doi:10.3982/TE5983

The mechanism displayed in the proof of Theorem 3 admits an unwanted Nash equilibrium in an admitted instance. The existential conclusion of Theorem 3 is not refuted.

  • Findings1 claim
  • Updated7 November 2026 · version 1.0

Claim · construction · main result · p. 1299; 1310–1311

Theorem 3 proof construction

Construction fails

The displayed mechanism can select an outcome outside F at a pure Nash equilibrium.

Theorem 3 proof construction. The four-rule message mechanism displayed in the proof of Theorem 3 implements F under the theorem's hypotheses for every admissible integer 1 ≤ k < n/2.

Assumptions
at least three agents; 1 ≤ k < n/2; strong comonotonicity; safe no-veto; the published priority-ordered Rules (i)–(iv)
Scope of the claim
Every admitted environment satisfying the hypotheses of Theorem 3 and every admissible safety level k.

What was found

With one state, outcomes {a,b}, F={b}, three agents and k=1, let agents 1 and 2 prefer b to a and agent 3 prefer a to b. At messages ((a,s,1),(a,s,1),(b,s,1)), the printed rules select a, outside F. The two agents who prefer b cannot profitably change the outcome by switching their report, and agent 3 already receives her preferred outcome.

What was tested

The minimal three-agent witness was checked against the published Rules (i)–(iv), the theorem's stated assumptions and the legal unilateral reports. Historical finite checks and a separate informed AI validation corroborate the construction failure.

Does not establish

  • The existential conclusion of Theorem 3 is not claimed to be false.
  • The record does not claim that no alternative mechanism can safely implement F.
  • The record does not publish or assess any private proposed correction.

Repair

No repair proposed

Verification

  • Separate AI recheckOct 2026 · informed. A separate informed AI validation checked the analytic failure family against the printed mechanism.
  • Reproduced by the researcherNot done.
  • External human verificationNot done.
  • Written author agreementNot given.
  • Qualifying human confirmation (private)Oct 2026. A qualifying human confirmation is recorded in the private research file. Its source and correspondence are not disclosed.

Confirmed: 2 kinds of check, 1 by a human. The standard requires two kinds, at least one by a human.

Source

Full check, pp. 1298–1299, 1310–1311. The definitions, Theorem 3, the displayed Rules (i)–(iv) and the decisive proof step were checked on rendered pages of the publisher-hosted version of record.

Authors and corrections

Authors
Not disclosed.
Correction
None published.

History

  1. October 2026Construction defect identified and separately rechecked
  2. 31 October 2026Full published-version source check completed
  3. 7 November 2026Record version 1.0 released

Versions

  1. Version 1.07 November 2026First release.

Released versions are never edited; each keeps its own address.

Use of AI in this case

AI systems were used for discovery and separate hostile rechecking. Confirmation also includes a qualifying human check recorded privately. Private correspondence is not disclosed, and AI agreement is not treated as human verification.