grad-contract-theory
用契約理論設計道德風險與逆選擇下誘因相容的薪酬和契約
中文翻譯
--- name: "grad-contract-theory" description: "用契約理論設計在道德風險與逆選擇下仍能誘因相容的協議。當使用者需要設計委託人與代理人的契約、評估薪酬方案，或分析雙方無法事前寫明所有情況的不完全契約問題時，就用這個 skill。" metadata: category: "WP-27 賽局與制度經濟" tags: ["contract-theory", "moral-hazard", "adverse-selection", "principal-agent", "incentive-design", "Hart", "Holmstrom", "incomplete-contracts"] --- # Contract Theory：道德風險、逆選擇與誘因設計 ## Overview 契約理論研究的是，在資訊不對稱的情況下，經濟行為者怎麼建構契約安排。兩個經典問題是道德風險（隱藏行動，代理人的努力程度看不到）和逆選擇（隱藏類型，代理人的特質只有他自己知道）。最佳契約要在委託人想分攤風險的需求，和激勵努力或誘出真實資訊的需求之間取得平衡。Hart 和 Holmstrom 在不完全契約與誘因設計上的貢獻，是現代契約理論的基礎。 ## When to Use - 設計員工或外包人員的薪酬、獎金或佣金結構 - 評估保險契約的道德風險（自負額、部分負擔）或逆選擇（篩選） - 設計品質無法觀察的合夥、加盟或採購契約 - 分析無法寫明所有狀態的不完全契約 ## When NOT to Use - 雙方資訊對稱，而且已經建立信任（沒有誘因問題） - 這是一次性的匿名交易，沒有契約執行機制 - 行為因素（互惠、內在動機）比金錢誘因影響更大 ## Assumptions ``` IRON LAW: The optimal contract balances risk-sharing against incentive provision — full insurance destroys incentives, full incentives impose unbearable risk. There is no contract that achieves first-best when information is asymmetric. ``` - 委託人風險中立，代理人風險趨避（標準設定） - 代理人的行動（努力）或類型是私有資訊 - 產出是代理人努力的雜訊訊號：x = f(e) + epsilon - 雙方都理性，而且能承諾遵守契約條款 - 法院可以驗證產出，但無法驗證努力（可契約性限制） ## Methodology **Step 1 — 分類資訊問題** 判斷核心問題是道德風險（簽約後的隱藏行動）、逆選擇（簽約前的隱藏類型），還是兩者都有。找出誰是委託人、誰是代理人。 **Step 2 — 列出限制式** 寫下：(1) 誘因相容限制（IC），代理人偏好採取預期的行動或揭露真實類型；(2) 參與限制（PC/IR），代理人接受這份契約勝過外部選項；(3) 有限責任（LL，若適用），支付不能低於零。 **Step 3 — 求解最佳契約** 道德風險的情況：在 IC 和 PC 限制下，最大化委託人的期望利潤。最佳工資函數 w(x) 滿足 Holmstrom 資訊性原則，也就是只有當產出能反映努力的資訊時，薪酬才該取決於產出。逆選擇的情況：設計一組契約菜單，讓代理人自我選擇（篩選）。預期底層會有扭曲（低類型的配置沒有效率），頂層則有效率。 **Step 4 — 評估完整性與重新談判** 檢查契約是完整的（涵蓋所有可驗證的情況）還是不完全的（剩餘權利很重要）。如果不完全，就套用 Hart 的產權途徑：把剩餘控制權分配給投資最重要的那一方。同時考慮契約能不能抵抗重新談判。 ## Output Format ```markdown ## Contract Design Analysis: [Context] ### Information Problem - **Type**: Moral hazard / Adverse selection / Both - **Principal**: [who] - **Agent**: [who] - **Hidden variable**: [effort level / agent type / quality] ### Constraints | Constraint | Expression | Binding? | |----------------------------|----------------------|----------| | Incentive Compatibility | | | | Participation (IR) | | | | Limited Liability | | | ### Optimal Contract Structure - **Fixed component**: [base salary / premium] - **Variable component**: [bonus / piece rate / deductible] - **Informativeness**: [which signals are used and why] ### First-Best vs. Second-Best Gap - **First-best outcome**: [what would happen with full information] - **Second-best distortion**: [what is sacrificed] - **Welfare loss**: [qualitative or quantitative] ### Recommendation [Contract terms and implementation guidance] ``` ## Gotchas - 多工任務（Holmstrom-Milgrom）：激勵一個可衡量的任務，會排擠無法衡量任務上的努力，強激勵可能適得其反 - 棘輪效應：如果委託人根據過去表現調整期望，代理人會策略性地在早期表現不佳 - 生涯關注（Holmstrom 1999）可以取代明確的誘因，年輕代理人即使沒有獎金，也會為了累積聲譽而努力 - 有限責任限制會把權力轉移給代理人，委託人可能得留下租金（效率工資） - 在重複關係中，關係型契約（自我執行，不靠法院強制）通常比正式契約更有效 - 外在誘因可能排擠內在動機（Benabou-Tirole），付錢給志工可能反而降低他們的努力 ## References - Holmstrom, B. (1979). "Moral Hazard and Observability." *Bell Journal of Economics*. - Hart, O. & Moore, J. (1990). "Property Rights and the Nature of the Firm." *Journal of Political Economy*. - Laffont, J.-J. & Martimort, D. (2002). *The Theory of Incentives: The Principal-Agent Model*. - Bolton, P. & Dewatripont, M. (2005). *Contract Theory*. MIT Press.
英文原文
--- name: "grad-contract-theory" description: "Apply contract theory to design incentive-compatible agreements under moral hazard and adverse selection. Use this skill when the user needs to structure principal-agent contracts, evaluate compensation schemes, or analyze incomplete contract problems where parties cannot specify all contingencies ex ante." metadata: category: "WP-27 賽局與制度經濟" tags: ["contract-theory", "moral-hazard", "adverse-selection", "principal-agent", "incentive-design", "Hart", "Holmstrom", "incomplete-contracts"] --- # Contract Theory: Moral Hazard, Adverse Selection, and Incentive Design ## Overview Contract theory studies how economic actors construct contractual arrangements in the presence of asymmetric information. The two canonical problems are moral hazard (hidden action — the agent's effort is unobservable) and adverse selection (hidden type — the agent's characteristics are private). The optimal contract balances the principal's desire for risk-sharing against the need to incentivize effort or truthful revelation. Hart and Holmstrom's contributions on incomplete contracts and incentive design form the modern foundation. ## When to Use - Designing compensation, bonus, or commission structures for employees or contractors - Evaluating insurance contracts for moral hazard (deductibles, copays) or adverse selection (screening) - Structuring partnerships, franchise agreements, or procurement contracts with unobservable quality - Analyzing incomplete contracts where not all states of the world can be specified ## When NOT to Use - Both parties have symmetric information and trust is established (no incentive problem) - The relationship is a one-shot anonymous transaction with no contractual enforcement - Behavioral factors (reciprocity, intrinsic motivation) dominate monetary incentives ## Assumptions ``` IRON LAW: The optimal contract balances risk-sharing against incentive provision — full insurance destroys incentives, full incentives impose unbearable risk. There is no contract that achieves first-best when information is asymmetric. ``` - The principal is risk-neutral; the agent is risk-averse (standard setup) - The agent's action (effort) or type is private information - Output is a noisy signal of the agent's effort: x = f(e) + epsilon - Both parties are rational and can commit to the contract terms - Courts can verify output but not effort (contractibility constraint) ## Methodology **Step 1 — Classify the Information Problem** Determine whether the core issue is moral hazard (hidden action after contracting), adverse selection (hidden type before contracting), or both. Identify who is the principal and who is the agent. **Step 2 — Specify Constraints** Write down: (1) the Incentive Compatibility constraint (IC) — the agent prefers the intended action/type revelation; (2) the Participation Constraint (PC/IR) — the agent accepts the contract over the outside option; (3) Limited Liability (LL) if applicable — payments cannot go below zero. **Step 3 — Solve the Optimal Contract** For moral hazard: maximize principal's expected profit subject to IC and PC. The optimal wage schedule w(x) satisfies the Holmstrom informativeness principle — pay should depend on output only insofar as it is informative about effort. For adverse selection: design a menu of contracts that induces self-selection (screening). Expect distortion at the bottom (inefficient allocation for low types) and efficiency at the top. **Step 4 — Assess Completeness and Renegotiation** Check whether the contract is complete (covers all verifiable contingencies) or incomplete (residual rights matter). If incomplete, apply Hart's property rights approach: allocate residual control rights to the party whose investment is most important. Consider renegotiation-proofness. ## Output Format ```markdown ## Contract Design Analysis: [Context] ### Information Problem - **Type**: Moral hazard / Adverse selection / Both - **Principal**: [who] - **Agent**: [who] - **Hidden variable**: [effort level / agent type / quality] ### Constraints | Constraint | Expression | Binding? | |----------------------------|----------------------|----------| | Incentive Compatibility | | | | Participation (IR) | | | | Limited Liability | | | ### Optimal Contract Structure - **Fixed component**: [base salary / premium] - **Variable component**: [bonus / piece rate / deductible] - **Informativeness**: [which signals are used and why] ### First-Best vs. Second-Best Gap - **First-best outcome**: [what would happen with full information] - **Second-best distortion**: [what is sacrificed] - **Welfare loss**: [qualitative or quantitative] ### Recommendation [Contract terms and implementation guidance] ``` ## Gotchas - Multi-tasking (Holmstrom-Milgrom): incentivizing one measurable task crowds out effort on unmeasurable tasks — strong incentives can be counterproductive - Ratchet effect: if the principal updates expectations based on past performance, the agent strategically underperforms early - Career concerns (Holmstrom 1999) can substitute for explicit incentives — young agents work hard to build reputation even without bonuses - Limited liability constraints shift power to the agent and can require the principal to leave rents (efficiency wages) - In repeated relationships, relational contracts (self-enforcing, not court-enforced) often dominate formal contracts - Intrinsic motivation can be crowded out by extrinsic incentives (Benabou-Tirole) — paying volunteers may reduce their effort ## References - Holmstrom, B. (1979). "Moral Hazard and Observability." *Bell Journal of Economics*. - Hart, O. & Moore, J. (1990). "Property Rights and the Nature of the Firm." *Journal of Political Economy*. - Laffont, J.-J. & Martimort, D. (2002). *The Theory of Incentives: The Principal-Agent Model*. - Bolton, P. & Dewatripont, M. (2005). *Contract Theory*. MIT Press.