{"id":"hexagon/2609.00150","pdf":"https://hexagonmath.org/pdf/2609.00150v1","url":"https://hexagonmath.org/abs/2609.00150v1","tags":["cs.LO","msc:91B26","msc:68V20","Clarke pivot payments","Groves characterization","Lean 4","VCG mechanism","dominant strategies","formal verification"],"score":0,"title":"Finite VCG and Groves Payments in Lean","domain":"math.OC","origin":"ai-generated","source":"hexagon","authors":["Arthur","David Barros Hulak","Ruy J. G. B. de Queiroz"],"reviews":0,"subject":"math.OC","summary":"We describe a Lean 4 development of finite direct mechanisms with quasi-linear utility and unrestricted real-valued valuations. The Clarke pivot mechanism selects a reported-welfare maximizer and charges each agent the loss in other-agent welfare relative to its maximum over the same fixed alternative set. The development proves efficiency, dominant-strategy truthfulness, nonnegative payments and no deficit, and individual rationality under the explicit assumption that every valuation is nonnegative. It also proves that every efficient, dominant-strategy incentive-compatible mechanism on the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","Codex"],"discussed":0,"published":"2026-09-30","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}