5D Library › Books › 5DL-B-027
机制设计、激励相容与谈判博弈的数学模型
从维克里拍卖、迈尔森-萨特思韦特不可能性定理到纳什议价与古典名实赏罚观考辨
Mechanism Design, Incentive Compatibility and the Game Theory of Negotiation: From Vickrey Auctions and the Myerson-Satterthwaite Theorem to Nash Bargaining, Read Beside Classical Chinese Legalist and Confucian Institutional Thought
DOI10.5281/zenodo.23765012摘要
谈判结束，双方都觉得满意，桌上却常常留着一大块谁都没拿到的价值；一个看似合理的考核指标，一年后数字漂亮、生意变差。本书用机制设计、拍卖理论、议价博弈与信息经济学考察规则本身如何塑造行为，以及好的规则在哪里必然受限。依次讨论：机制设计作为「逆向博弈论」与显示原理，「我切你选」的无嫉妒性（只保证每人一半，结果取决于谁掌握对方偏好的信息），公共品自愿捐献中的搭便车与克拉克枢纽机制（如实报告为占优策略，但税款不能退还、预算无法平衡）；维克里二价拍卖中报真值的弱占优性（程序在 1,030,301 种组合上验证），一价拍卖的压价是可推导的均衡策略 b = (n−1)v/n 而不是赌运气，收益等价定理的程序验证，以及 VCG 机制收入可能为零、随竞争者增加而下降、对落败者协调脆弱的弱点；迈尔森—萨特思韦特定理的四个条件与估值重叠前提，均匀分布下最好的机制只在 v ≥ c + 1/4 时成交、实现 9/64 ÷ 1/6 = 84.375% 的交易收益，查特吉—萨缪尔森线性均衡恰好达到这一上限但并非唯一均衡；纳什议价解与鲁宾斯坦轮流出价 x₁* = (1 − δ₂)/(1 − δ₁δ₂) 及两者的收敛，并核对后修正「筹码取决于 BATNA」：BATNA 决定底线，作为纳什威胁点时持续起作用，但在带外部选择的轮流出价中只有高于本来份额时才起作用（外部选择原则），持续改变份额的是耐心与谈判期间的内部收益；柠檬市场的价格螺旋、认证与斯宾塞信号的分离条件（单交叉、成本区间、可核查）及纯信号的社会浪费；古德哈特 1975 年原话与斯特拉森 1997 年通俗表述的区别、坎贝尔定律，以及可操纵指标的选择模型与随机审计允许更陡峭激励的多任务模型。
八章与《韩非子·定法》「循名而责实」、《二柄》同时惩罚「言大而功小」与「言小而功大」及韩昭侯「兼罪典衣与典冠」（出自《二柄》而非《定法》）、《管子·明法》「不淫意于法之外，不为惠于法之内」、《论语》「政者，正也」与「道之以德」、《孟子》「上下交征利而国危矣」并读，并明确古代法家服务于君主集权、现代机制设计服务于平等主体的自愿契约与公共福利；最后给出一份四步机制与议价核查表（双方 BATNA 量化、等待成本与现金流耐心审计、从口头保证切换为可核查信号、KPI 古德哈特漏洞红队测试），以及一项预注册双人随机对照试验方案：以两人组为随机化单位、两人接受同一条件，比较谈判前 10 分钟结构化准备表格与常规谈判技巧阅读，唯一主要结局为五议题模拟谈判的联合点数（未达成协议计为双方 BATNA 之和），每组 173 组可分析、随机化 193 组，共 772 人，判定规则写成代码。书中以标注框区分已发表的证据、可运行的 Python 计算（16 段程序，全部核对）、原典与作者的假说。本书不是法律意见；拍卖串通、围标等违法行为只作为机制弱点讨论，不提供操作方法。
关键词：机制设计；激励相容；显示原理；我切你选；无嫉妒分配；公共品；克拉克枢纽机制；维克里拍卖；一价拍卖；收益等价定理；VCG 机制；迈尔森—萨特思韦特定理；双边拍卖；纳什议价解；鲁宾斯坦议价；外部选择原则；谈判协议的最佳替代方案；柠檬市场；信号理论；古德哈特定律
Abstract
A negotiation ends with both sides satisfied, yet a large piece of value is often left on the table; a reasonable-looking performance metric produces beautiful numbers and a worse business a year later. This book uses mechanism design, auction theory, bargaining theory and the economics of information to examine how rules themselves shape behaviour, and where even good rules meet unavoidable limits. It covers mechanism design as "reverse game theory" and the revelation principle; the envy-freeness of "I cut, you choose" (which guarantees each person only half, with the outcome depending on who knows the other's preferences); free-riding in voluntary public-good contributions and the Clarke pivot mechanism (truthful reporting is dominant, but taxes cannot be returned and the budget cannot balance); the weak dominance of truthful bidding in Vickrey's second-price auction (verified by program across 1,030,301 combinations), bid shading in first-price auctions as a derivable equilibrium strategy b = (n−1)v/n rather than a gamble, a program check of revenue equivalence, and the weaknesses of VCG, whose revenue can be zero, can fall as bidders are added and is fragile against coordination among losers; the four conditions of the Myerson–Satterthwaite theorem and its overlap assumption, with the best mechanism in the uniform case trading only when v ≥ c + 1/4 and realising 9/64 ÷ 1/6 = 84.375 % of the gains from trade, a bound attained by the linear Chatterjee–Samuelson equilibrium, which is not the only equilibrium; the Nash bargaining solution, Rubinstein's alternating offers x₁* = (1 − δ₂)/(1 − δ₁δ₂) and their convergence, with a checked correction of "your leverage depends on your BATNA": a BATNA sets the bottom line and acts continuously as a Nash threat point, but in alternating offers with an outside option it matters only when it exceeds one's share anyway (the outside option principle), while patience and payoffs during the talks move shares continuously; the price spiral of the market for lemons, certification, the separating conditions for Spence signals (single crossing, a cost range, verifiability) and the social waste of pure signals; the difference between Goodhart's 1975 wording and Strathern's 1997 popular version, Campbell's law, a selection model of manipulable metrics and a multitask model in which random audits permit steeper incentives.
The eight chapters are read beside the Han Feizi on "holding names to account for reality", the "Two Handles" chapter's punishment of both "large words, small results" and "small words, large results" and its story of Marquis Zhao punishing both the keeper of robes and the keeper of caps (from "The Two Handles", not "Defining the Law"), the Guanzi's "not letting intentions roam outside the law, nor granting favours within the law", the Analects' "to govern is to correct" and "lead them with virtue", and Mencius's "when superiors and inferiors compete for profit, the state is in danger", stating clearly that ancient Legalism served the ruler's centralised power while modern mechanism design serves voluntary contracts between equals and public welfare. They end with a four-step mechanism and bargaining checklist (quantifying both sides' BATNAs, auditing the cost of waiting and cash-flow patience, replacing verbal assurances with verifiable signals, red-teaming KPIs for Goodhart leaks) and a pre-registered dyad-randomised controlled trial in which both members of each dyad receive the same condition, comparing a 10-minute structured preparation form with reading standard negotiation tips; the single primary outcome is joint points in a five-issue simulated negotiation (impasse scored as the sum of both BATNAs), with 173 analysable and 193 randomised dyads per arm, 772 people in all, and a decision rule written as code. Marked boxes separate published evidence, runnable Python calculations (16 programs, all checked), classical sources and the author's hypotheses. This book is not legal advice; bid rigging, collusive tendering and other unlawful practices are discussed only as weaknesses of mechanisms, and no method for them is given.
Keywords: mechanism design; incentive compatibility; revelation principle; cut and choose; envy-free division; public goods; Clarke pivot mechanism; Vickrey auction; first-price auction; revenue equivalence; VCG mechanism; Myerson–Satterthwaite theorem; double auction; Nash bargaining solution; Rubinstein bargaining; outside option principle; BATNA; market for lemons; signalling; Goodhart's law
目录 · Contents
- 序：先定规则，再谈输赢English 中文Preface: Set the Rules Before You Play
- 第一章 逆向博弈论：激励相容与显示原理English 中文Chapter 1 Reverse Game Theory: Incentive Compatibility and the Revelation Principle
- 第二章 拍卖：维克里、收益等价与 VCG 的孤独English 中文Chapter 2 Auctions: Vickrey, Revenue Equivalence and the Loneliness of VCG
- 第三章 迈尔森—萨特思韦特不可能性定理English 中文Chapter 3 The Myerson–Satterthwaite Impossibility Theorem
- 第四章 议价：纳什、鲁宾斯坦与 BATNA 的真正作用English 中文Chapter 4 Bargaining: Nash, Rubinstein and What a BATNA Really Does
- 第五章 柠檬市场与昂贵的信号English 中文Chapter 5 Lemons and Costly Signals
- 第六章 古德哈特定律：当指标变成目标English 中文Chapter 6 Goodhart's Law: When a Measure Becomes a Target
- 第七章 原典并读：循名责实、二柄与「政者，正也」English 中文Chapter 7 Reading the Classics: Names and Reality, the Two Handles and "To Govern Is to Correct"
- 第八章 实践与预注册试验English 中文Chapter 8 Practice and a Pre-registered Trial
How to cite · 引用
Fan, Y. (2026). Mechanism Design, Incentive Compatibility and the Game Theory of Negotiation: From Vickrey Auctions and the Myerson-Satterthwaite Theorem to Nash Bargaining, Read Beside Classical Chinese Legalist and Confucian Institutional Thought [机制设计、激励相容与谈判博弈的数学模型] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23765012
BibTeX
@book{fan2026mechanism,
title = {{Mechanism Design, Incentive Compatibility and the Game Theory of Negotiation}: From Vickrey Auctions and the Myerson-Satterthwaite Theorem to Nash Bargaining, Read Beside Classical Chinese Legalist and Confucian Institutional Thought},
author = {Fan, Yafu},
year = {2026},
publisher = {5D Library},
edition = {Version 1.0.0},
doi = {10.5281/zenodo.23765012},
url = {https://doi.org/10.5281/zenodo.23765012},
note = {Chinese title: 机制设计、激励相容与谈判博弈的数学模型}
}
| DOI | https://doi.org/10.5281/zenodo.23765012 |
|---|---|
| ORCID | https://orcid.org/0009-0004-3519-1203 |
| 5D Library ID | 5DL-B-027 |
| 版本 Version | 1.0.0 · 中英双语版 Bilingual edition |
| 出版日期 Date | 2026-10-29 |
| 网址 Online | https://5dlibrary.com/books/mechanism-design-negotiation/ |
| SHA-256 · mechanism-design-negotiation_bilingual_v1.0.0.pdf | 47217aab471991d890a7f993c84342eaa9c92a3fd019d82c9f0bea4e44a22adc |
| SHA-256 · mechanism-design-negotiation_en_v1.0.0.pdf | 7dc0860e01f8e8a8a82a1b56d04053a2fda5f4592e0778f263dafc2eae628b02 |
| SHA-256 · mechanism-design-negotiation_zh_v1.0.0.pdf | cc3c01d41e5811e05fed001f59336d7bdbddf855397fa9fef01484e5d02a75c9 |
| Licence · 许可 | Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). https://creativecommons.org/licenses/by-nc-nd/4.0/ |
Disclosure. The author uses the works of 5D Library, including this book, as the methodological basis of his community courses, the 5D Ascension Cards (Dimensional Shift Card Decks) and the Yafu AI knowledge base, and therefore has a commercial interest in the subject of this book. In addition, the author founded and runs Asia Influencer X and Yafu Global, whose day-to-day business involves commercial negotiation and contract design with brands and partners, and he therefore has a direct commercial interest in the subject of this book; the book uses no client data from these businesses, and the Chapter 8 trial does not recruit from their clients. The book promotes no course, card deck or service; the Chapter 8 trial is designed to be run and analysed by researchers independent of the author's business and does not recruit from the author's community, students or customers; all the code and the study protocol are published openly for anyone to check.