grad-mechanism-design
用機制設計為拍賣、投票和配對設計誘因相容的規則
中文翻譯
--- name: "grad-mechanism-design" description: "用機制設計（反向賽局理論）為分配問題設計誘因相容的規則。當使用者需要設計拍賣、投票系統或配對市場，或要評估某個提議的機制是否滿足誘因相容與個人理性限制時，就用這個 skill。" metadata: category: "WP-27 賽局與制度經濟" tags: ["mechanism-design", "incentive-compatibility", "revelation-principle", "Myerson-Satterthwaite", "auction-design", "matching-markets"] --- # Mechanism Design：反向賽局理論與誘因相容 ## Overview 機制設計是賽局理論的工程面：不是分析給定的賽局，而是設計規則，讓自利的行為者產生期望的結果。核心工具是顯示原理，它指出任何可實施的結果，都能透過一個讓說真話成為最佳選擇的直接機制來達成。這個領域支撐了拍賣設計、投票系統、配對市場和監管框架。 ## When to Use - 設計參與者擁有私有資訊的分配規則（拍賣、配對、資源分享） - 評估某個提議的制度或平台，是否誘使人們誠實行事 - 評估效率、預算平衡和參與限制之間的取捨 ## When NOT to Use - 行為者完全合作，沒有私有資訊（不存在誘因問題） - 環境太複雜，無法為行為者的類型建模（改用行為實驗） - 你要的是快速的捷思法，不是正式的保證 ## Assumptions ``` IRON LAW: A mechanism is incentive-compatible ONLY if truth-telling is a dominant strategy — no mechanism can simultaneously maximize efficiency, budget balance, and individual rationality (Myerson-Satterthwaite theorem). ``` - 行為者是理性的，並最大化期望效用 - 每個行為者都有私有資訊（類型），來自已知的先驗分配 - 設計者在行為者行動之前，就承諾機制規則 - 移轉（支付）是可行的，並適用準線性效用 ## Methodology **Step 1 — 定義設計問題** 指明行為者的集合、他們的類型空間、結果空間，以及你想實施的社會選擇函數。找出目標：效率、收益、公平，或加權組合。 **Step 2 — 套用顯示原理** 把注意力限縮在直接顯示機制。對每個行為者，機制會請他報告類型，並把報告的組合對應到結果和移轉。檢查誠實報告是否構成 Bayesian Nash 均衡（BNE-IC）或占優策略均衡（DSIC）。 **Step 3 — 驗證限制式** 檢查三個核心限制：(1) 誘因相容，沒有行為者能靠謊報獲益；(2) 個人理性，每個行為者參與的處境至少不比不參與差；(3) 預算平衡，設計者不會虧損。套用 Myerson-Satterthwaite 判斷哪些限制可以並存。 **Step 4 — 刻畫與最佳化** 用包絡定理，從分配規則推導支付規則。在有效的限制式下，最佳化目標。報告哪些取捨是無法避免的。 ## Output Format ```markdown ## Mechanism Design Analysis: [Context] ### Design Problem - **Agents**: [who participates] - **Type space**: [private information each agent holds] - **Outcome space**: [possible allocations] - **Objective**: [efficiency / revenue / fairness] ### Proposed Mechanism - **Allocation rule**: [how outcomes map to reports] - **Payment rule**: [transfers as function of reports] ### Constraint Verification | Constraint | Satisfied? | Notes | |--------------------------|------------|-------| | Incentive Compatibility | Yes / No | | | Individual Rationality | Yes / No | | | Budget Balance | Yes / No | | ### Impossibility Trade-offs [Which constraints conflict per Myerson-Satterthwaite; what the designer must sacrifice] ### Recommendation [Chosen mechanism and rationale] ``` ## Gotchas - 顯示原理保證直接機制存在，但對實務上的簡潔性什麼都沒說，現實中的機制常因為行為上的理由用間接形式 - Myerson-Satterthwaite 不可能定理適用於私有價值的雙邊交易，多邊情境可能逃過它 - DSIC 比 BNE-IC 更強，很多實務上的機制（例如 VCG）是 DSIC，但可能違反預算平衡 - 行為者類型之間的相關性可以被利用（Cremer-McLean）來榨取全部剩餘，但需要很強的分配知識 - 在未被占優的策略下實施、完全實施和部分實施是不同的解概念，要說明你指的是哪一種 - 有行為特徵的行為者（有限理性、惡意、公平考量）會破壞理論上誘因相容的機制 ## References - Myerson, R. (1981). "Optimal Auction Design." *Mathematics of Operations Research*. - Myerson, R. & Satterthwaite, M. (1983). "Efficient Mechanisms for Bilateral Trading." *Journal of Economic Theory*. - Mas-Colell, A., Whinston, M. & Green, J. (1995). *Microeconomic Theory*, Ch. 23. - Borgers, T. (2015). *An Introduction to the Theory of Mechanism Design*.
英文原文
--- name: "grad-mechanism-design" description: "Apply mechanism design (reverse game theory) to engineer incentive-compatible rules for allocation problems. Use this skill when the user needs to design auctions, voting systems, or matching markets, or when evaluating whether a proposed mechanism satisfies incentive compatibility and individual rationality constraints." metadata: category: "WP-27 賽局與制度經濟" tags: ["mechanism-design", "incentive-compatibility", "revelation-principle", "Myerson-Satterthwaite", "auction-design", "matching-markets"] --- # Mechanism Design: Reverse Game Theory and Incentive Compatibility ## Overview Mechanism design is the engineering side of game theory: instead of analyzing given games, you design the rules so that self-interested agents produce a desired outcome. The central tool is the revelation principle, which shows that any implementable outcome can be achieved by a direct mechanism where truth-telling is optimal. The field underpins auction design, voting systems, matching markets, and regulatory frameworks. ## When to Use - Designing allocation rules (auctions, matching, resource sharing) where participants have private information - Evaluating whether a proposed institution or platform incentivizes truthful behavior - Assessing trade-offs between efficiency, budget balance, and participation constraints ## When NOT to Use - Agents are fully cooperative with no private information (no incentive problem exists) - The environment is too complex to model agent types (use behavioral experiments instead) - You need a quick heuristic rather than a formal guarantee ## Assumptions ``` IRON LAW: A mechanism is incentive-compatible ONLY if truth-telling is a dominant strategy — no mechanism can simultaneously maximize efficiency, budget balance, and individual rationality (Myerson-Satterthwaite theorem). ``` - Agents are rational and maximize expected utility - Each agent has private information (type) drawn from a known prior distribution - The designer commits to the mechanism rules before agents act - Transfers (payments) are feasible and quasi-linear utility applies ## Methodology **Step 1 — Define the Design Problem** Specify the set of agents, their type spaces, the outcome space, and the social choice function you want to implement. Identify the objective: efficiency, revenue, fairness, or a weighted combination. **Step 2 — Apply the Revelation Principle** Restrict attention to direct revelation mechanisms. For each agent, the mechanism asks for a reported type and maps the profile of reports to an outcome and transfers. Check whether truthful reporting constitutes a Bayesian Nash equilibrium (BNE-IC) or dominant strategy equilibrium (DSIC). **Step 3 — Verify Constraints** Check three core constraints: (1) Incentive Compatibility — no agent gains by misreporting; (2) Individual Rationality — each agent is at least as well off participating as not; (3) Budget Balance — the designer does not run a deficit. Apply Myerson-Satterthwaite to determine which constraints can co-exist. **Step 4 — Characterize and Optimize** Use the envelope theorem to derive the payment rule from the allocation rule. Optimize the objective subject to binding constraints. Report which trade-offs are unavoidable. ## Output Format ```markdown ## Mechanism Design Analysis: [Context] ### Design Problem - **Agents**: [who participates] - **Type space**: [private information each agent holds] - **Outcome space**: [possible allocations] - **Objective**: [efficiency / revenue / fairness] ### Proposed Mechanism - **Allocation rule**: [how outcomes map to reports] - **Payment rule**: [transfers as function of reports] ### Constraint Verification | Constraint | Satisfied? | Notes | |--------------------------|------------|-------| | Incentive Compatibility | Yes / No | | | Individual Rationality | Yes / No | | | Budget Balance | Yes / No | | ### Impossibility Trade-offs [Which constraints conflict per Myerson-Satterthwaite; what the designer must sacrifice] ### Recommendation [Chosen mechanism and rationale] ``` ## Gotchas - The revelation principle guarantees existence of a direct mechanism but says nothing about practical simplicity — real-world mechanisms often use indirect formats for behavioral reasons - Myerson-Satterthwaite impossibility applies to bilateral trade with private values; multilateral settings may escape it - DSIC is stronger than BNE-IC; many practical mechanisms (e.g., VCG) are DSIC but may violate budget balance - Correlation among agent types can be exploited (Cremer-McLean) to extract full surplus, but requires strong distributional knowledge - Implementation in undominated strategies vs. full implementation vs. partial implementation are distinct solution concepts — specify which you mean - Behavioral agents (bounded rationality, spite, fairness concerns) can break mechanisms that are theoretically incentive-compatible ## References - Myerson, R. (1981). "Optimal Auction Design." *Mathematics of Operations Research*. - Myerson, R. & Satterthwaite, M. (1983). "Efficient Mechanisms for Bilateral Trading." *Journal of Economic Theory*. - Mas-Colell, A., Whinston, M. & Green, J. (1995). *Microeconomic Theory*, Ch. 23. - Borgers, T. (2015). *An Introduction to the Theory of Mechanism Design*.