EC487 Redo
使用范围
- 已忽略：
AT/文件夹全部内容。 - 已使用：
EC487 - Syllabus 2026.pdf、lecture slides/、problem sets/EC487_WT_Pset1.pdf到EC487_WT_Pset9.pdf、solutions/中已有的 WT solutions。 - 注意：
solutions/中没有找到 Pset5 的 solution，所以 Pset5 的“主要解题方法”依据题面和对应课件整理，不把不存在的答案文件当作依据。 - 课件页码按 PDF 页码记录；若题目是 Problem Set 的扩展题，关联课件列给出最接近的 current WT lecture source。
Problem Set 重做总表
| 题目 | 题号(a,b,c,d) | 考点 | 主要解题方法 | 关联课件 | 重做 |
|---|---|---|---|---|---|
| PS1 Q1 Cournot Game with Private Costs | Q1(a) | Bayesian Nash Equilibrium (BNE) 定义 | 明确类型、策略函数、信念和每个类型的最优反应条件。 | Lecture 1, p11; Lecture 1, p15 | Done |
| PS1 Q1 Cournot Game with Private Costs | Q1(b) | 私人成本下的 Cournot BNE | 对 firm 2 的两个类型分别写 FOC；firm 1 对 firm 2 的期望产量作最优反应，联立求解。 | Lecture 1, p15-p19 | Done |
| PS1 Q1 Cournot Game with Private Costs | Q1(c) | 成本不确定性与利润比较静态 | 代入 theta=1/2、cH=b+chat、cL=b-chat，对利润关于 chat 做比较静态并解释信息不确定性。 | Lecture 1, p11; Lecture 1, p15-p19 | Done |
| PS1 Q2 Purification | Q2(a) | 不完全信息 game 的纯策略阈值均衡 | 把类型扰动写进 payoff difference，找让玩家无差异的 cutoff，再验证双方最优反应。 | Lecture 1, p11-p19 | Done |
| PS1 Q2 Purification | Q2(b) | Harsanyi purification 与 mixed equilibrium 极限 | 计算各玩家采取偏好动作的概率，令 epsilon -> 0，对照完全信息 Battle of the Sexes 的混合均衡。 | Lecture 1, p15-p19 | Done |
| PS1 Q2 Purification | Q2(c) | 混合策略与微小 payoff 扰动 | 用文字说明：完全信息混合均衡可看作近似不完全信息博弈纯策略均衡的极限。 | Lecture 1, p11-p15 | 考试应该不会考 |
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(a) | Common value auction payoff | 按是否赢、是否平局分别写 payoff；注意 winner pays own bid。 | Lecture 7, p4-p5; Lecture 1, p11 | done |
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(b) | 单调策略下的期望 payoff | 用对手策略反函数把“赢的事件”写成 t2 <= sigma_2^{-1}(b1)，再对信号积分。 | Lecture 7, p9-p10; Lecture 1, p15 | done |
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(c) | bidding FOC | 对 bid 或 implied cutoff 求导，一阶条件连接边际胜率和条件期望价值。 | Lecture 7, p9-p10 | done |
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(d) | 对称递增均衡 bidding function | 施加 sigma_1=sigma_2，把 FOC 化成微分方程并用边界条件求唯一解。 | Lecture 7, p9-p11 | done |
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(e) | Winner’s curse | 比较 E[v given t1] 与 E[v given t1, winning]，说明赢本身传递对手 signal 较低的信息。 | Lecture 7, p9-p11; Lecture 1, p11 | done |
| PS2 Q1 Global Games | Q1(a) | cutoff equilibrium | 猜测阈值策略 Invest iff xi > x*，用条件正态信念让 cutoff type 无差异。 | Lecture 1, p20-p29 | Higher-order belief 不在考纲里，可以省略 |
| PS2 Q1 Global Games | Q1(b) | Risk dominance | 在完全信息 2x2 协调博弈中令对手均匀混合，比较 Invest 和 Not Invest 的期望 payoff。 | Lecture 1, p20-p29 | |
| PS2 Q1 Global Games | Q1(c) | vanishing noise selection | 令 sigma -> 0，解释 incomplete information equilibrium 如何选择 risk-dominant equilibrium。 | Lecture 1, p20-p29 | |
| PS2 Q2 Disclosure Game | Q2 | Signalling game, weak PBE, unraveling | 用 firm 的最优工资等于 posterior mean；再用最高未披露类型的偏离证明几乎所有类型都会 disclose。 | Lecture 2, p4-p6; Lecture 2, p14-p15 | done |
| PS3 Q1 Spence Signalling | Q1(1) | 低类型最喜欢的 equilibrium | 比较低类型在 pooling 与 separating 中的 wage minus education cost；优先找最低教育成本的 pooling。 | Lecture 2, p14-p22 | |
| PS3 Q1 Spence Signalling | Q1(2) | 高类型最喜欢的 equilibrium | 比较 least-cost separating 与 pooling payoff，注意高类型教育成本较低但 pooling 有平均工资。 | Lecture 2, p14-p22 | |
| PS3 Q1 Spence Signalling | Q1(3) | firm 最喜欢的 equilibrium | firm payoff 是 wage 对 productivity 的 squared loss；比较 pooling 和 separating 的信息精度。 | Lecture 2, p14-p22 | |
| PS3 Q1 Spence Signalling | Q1(4) | Pareto-undominated equilibria | 枚举 pooling 与 separating outcome，删去被所有相关方弱支配且至少一方严格受益的 equilibrium。 | Lecture 2, p14-p22 | |
| PS3 Q2 Partial Pooling in Spence Signalling | Q2(a) | partial pooling equilibrium construction | 设计 beliefs、工资和混合概率，让 eM 处 firm posterior 支持 pooling，同时让两类型在各自混合支持上无差异。 | Lecture 2, p14-p22; Lecture 2, p23-p26 | |
| PS3 Q2 Partial Pooling in Spence Signalling | Q2(b) | Intuitive Criterion | 找一个 off-path education level，判断哪些类型可能从偏离中获益，再看合理 beliefs 是否破坏该 equilibrium。 | Lecture 2, p23-p34 | |
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(1) | Beer-Quiche pooling equilibrium existence | 对 beer pooling 和 quiche pooling 分别写 receiver posterior 与 best response，检查 sender 偏离。 | Lecture 2, p7-p13; Lecture 2, p27-p28 | |
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(2) | pooling 不存在时的 pure PBE | 检查 separating 和 pooling 候选；用偏离激励排除纯策略 equilibrium。 | Lecture 2, p7-p13 | |
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(3) | mixed-strategy PBE | 令 receiver 在 fight/run 间无差异，反推出 wimpy type 的混合概率；再验证 surly type。 | Lecture 2, p7-p13 | |
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(4) | Intuitive Criterion refinement | 对混合均衡中的 off-path 或低概率路径应用 equilibrium dominance 和合理 beliefs。 | Lecture 2, p23-p28 | |
| PS4 Q1 Characterizing Interval Equilibria in Cheap Talk | Q1 | cheap talk interval recurrence | 用相邻 interval 边界类型的 sender indifference，推出长度递推式 theta_{k+1}-theta_k = theta_k-theta_{k-1}+4b。 | Lecture 3, p15-p21 | |
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(1) | receiver ex-ante payoff | 对每个 interval 用 receiver posterior mean 作为 action，把平方损失按 interval 积分求期望。 | Lecture 3, p7; Lecture 3, p15-p21 | |
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(2) | sender payoff 与 receiver payoff 的 aligned ranking | 把 sender ideal point theta+b 展开，说明 equilibrium payoff 排序和 receiver information precision 同向。 | Lecture 3, p5-p7; Lecture 3, p15-p21 | |
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(3) | bias b=1/12 下的 equilibrium set | 由 interval existence 条件求最大 interval 数，列出各 n 的 thresholds 与 ex-ante payoff。 | Lecture 3, p20-p21 | |
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(4) | bias b'=1/24 下的 equilibrium set | 重复 interval recurrence 和 existence 条件，比较可支持的信息精度。 | Lecture 3, p20-p21 | |
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(5) | endogenous bias preference | 用 Q2 payoff 排序判断 sender 与 receiver 是否偏好更小 bias。 | Lecture 3, p18-p22 | |
| PS4 Q3 Cheap Talk with Non-Uniform State Distribution | Q3(1) | non-uniform distribution 下两 interval equilibrium | 把 receiver action 改成 conditional mean under F(x)=x^rho，再写边界类型无差异。 | Lecture 3, p15-p21 | |
| PS4 Q3 Cheap Talk with Non-Uniform State Distribution | Q3(2) | n interval generalization | 对每个 interval 计算 conditional mean，逐段施加相邻边界 indifference 与存在条件。 | Lecture 3, p15-p21 | |
| PS5 Q1 Reputation | Q1(a) | complete-information sequential bargaining | 类型已知时做 backward induction；rational seller 与 behavioral seller 分开求 buyer offer。 | Lecture 1, p30-p40; Lecture 3, p23-p25 | |
| PS5 Q1 Reputation | Q1(b) | no history observation 的 weak PBE | 因每期 buyer belief 不随历史更新，逐期按 prior 最优报价并验证 seller 接受规则。 | Lecture 3, p23-p31 | |
| PS5 Q1 Reputation | Q1(c) | reputation beliefs and buyer optimal offer | 用给定 belief-consistency rule 更新 rational posterior；比较 offer 0 和 offer 1 的 expected payoff。 | Lecture 3, p23-p31; Lecture 1, p36-p40 | |
| PS5 Q1 Reputation | Q1(d) | two-price restriction and weak PBE existence | 在 p in {0,1} 下逐个候选 equilibrium 验证 sequential rationality 与 beliefs consistency。 | Lecture 3, p27-p31 | |
| PS5 Q2 Positive Selection | Q2(a) | positive selection | 因 r(theta) strictly decreasing，高类型更愿意进入劳动市场；用 participation set 单调性证明。 | Lecture 4, p4-p11 | |
| PS5 Q2 Positive Selection | Q2(b) | competitive equilibrium efficiency | 当所有类型在 firm 的 product 高于 outside option 时，市场进入选择不会排除有效交易。 | Lecture 4, p5-p8 | |
| PS5 Q2 Positive Selection | Q2(c) | excessive employment relative to Pareto optimum | 比较 competitive wage 条件与 planner 条件；positive selection 下雇佣边际类型可能社会价值为负。 | Lecture 4, p6-p11 | |
| PS5 Q3 Certification in Adverse Selection | Q3(a) | adverse selection market equilibrium | 在 r(theta)=alpha theta、theta~U[0,2] 下求接受 employment 的 cutoff 与 zero-profit wage fixed point。 | Lecture 4, p4-p11 | |
| PS5 Q3 Certification in Adverse Selection | Q3(b) | certification splits markets | 把 certified 与 uncertified workers 分成两个 pools，各自用 conditional mean productivity 定 wage。 | Lecture 4, p6-p11; Lecture 4, p12-p17 | |
| PS5 Q3 Certification in Adverse Selection | Q3(c) | employment-maximizing certification threshold | 写出 employment measure as function of threshold，求使就业规模最大的 thetahat。 | Lecture 4, p8-p11 | |
| PS5 Q3 Certification in Adverse Selection | Q3(d) | paid certification equilibrium | 加入 certification price 后，把 worker participation/certification incentive 与 firm zero profit 联立。 | Lecture 4, p12-p17 | |
| PS5 Q3 Certification in Adverse Selection | Q3(e) | intermediary profit maximization | 写 intermediary demand for certification，最大化 price * certified mass。 | Lecture 4, p12-p17 | |
| PS6 Q1 Limited Liability | Q1(a) | hidden action with limited liability | 写 principal 的 cost-minimization program：min expected wage subject to IC for H and s_i >= 0。 | Lecture 5, p4-p5; Lecture 5, p12-p18 | |
| PS6 Q1 Limited Liability | Q1(b) | MLRP and bang-bang wage | 用 IC 的 likelihood-ratio representation；MLRP 说明把奖励集中在最高 outcome 最便宜。 | Lecture 5, p15-p18 | |
| PS6 Q2 Optimal Contract in Closed Form | Q2(a) | first-best effort choice | effort 可合约时比较 high effort 的 expected output gain 与 effort cost；wage 只需满足 participation。 | Lecture 5, p6-p9 | |
| PS6 Q2 Optimal Contract in Closed Form | Q2(b) | moral hazard optimal wage | 写 IR 和 IC；通常令低 output wage 最低，高 output wage 提供 incentive spread。 | Lecture 5, p10-p20 | |
| PS6 Q2 Optimal Contract in Closed Form | Q2(c) | induce high effort condition | 比较 inducing high effort 的 profit 与 inducing low effort 的 profit，注意 incentive rent/risk cost。 | Lecture 5, p18-p20 | |
| PS6 Q2 Optimal Contract in Closed Form | Q2(d) | informativeness and comparative statics | 对 expected profit 关于 p1、p0 比较静态；解释 signal informativeness 提高会降低激励成本。 | Lecture 5, p21-p23 | |
| PS6 Q2 Optimal Contract in Closed Form | Q2(e) | limited liability floor | 将 wage floor w(y)>=L 加入约束，检查原解是否违反；若违反则把低 output wage 设到 floor 并重算。 | Lecture 5, p15-p20 | |
| PS7 Q1 Uniformly Distributed Errors | Q1(a) | first-best contract with observable effort | effort 可观察时给 flat wage insurance，选择 effort 使 expected surplus 最大。 | Lecture 5, p6-p9; Lecture 5, p24-p28 | |
| PS7 Q1 Uniformly Distributed Errors | Q1(b) | full implementation despite hidden effort | 利用 uniform support shift 构造 wage schedule，让 output perfectly reveals effort interval 或让 IC 不扭曲。 | Lecture 5, p21-p24; Lecture 5, p24-p28 | |
| PS7 Q2 Simple Screening Example | Q2(a) | FOC and complementary slackness | 在两类型 screening Lagrangian 中对 qL,qH,pL,pH 求 FOC，并写 IC、IR、nonnegativity 的 slackness。 | Lecture 6, p6-p11 | |
| PS7 Q2 Simple Screening Example | Q2(b) | corner solution with qL=0 | 当 thetaL < alphaH thetaH 且 c'(0)=0，显式处理 qL>=0 binding，求 multipliers。 | Lecture 6, p8-p11 | |
| PS7 Q2 Simple Screening Example | Q2(c) | positive marginal cost at zero | 若 c'(0)>0，重新判断 qL=0 的 FOC/KKT 条件，说明低类型 allocation 可能仍在角点但 multiplier 变化。 | Lecture 6, p8-p11 | |
| PS8 Q1 Taxation Principle | Q1(a) | monotonicity of price when allocation increases | 用 IC constraints 交叉相加，推出 allocation monotonicity 与 payment monotonicity。 | Lecture 6, p15-p18 | |
| PS8 Q1 Taxation Principle | Q1(b) | flat allocation implies flat payment | 若 q(theta1)=q(theta2)，双向 IC 夹逼得到 p(theta1)=p(theta2)。 | Lecture 6, p15-p18 | |
| PS8 Q1 Taxation Principle | Q1(c) | Taxation Principle | 把 direct mechanism outcome 写成 nonlinear price schedule P(q)，说明 truthful choice 等价于从菜单中自选。 | Lecture 6, p12-p18 | |
| PS8 Q2 Optimal Mechanism in Closed Form | Q2(a) | continuum screening under uniform distribution | 计算 virtual value Psi(theta)=theta-(1-F)/f；regular case 下令 c'(q)=Psi(theta) 并用 envelope formula 求 payment。 | Lecture 6, p15-p23 | |
| PS8 Q2 Optimal Mechanism in Closed Form | Q2(b) | non-uniform density and ironing check | 分段计算 F、f、virtual value；检查 monotonicity，若不 regular 则识别 ironing 区间。 | Lecture 6, p21-p23 | |
| PS9 Q1 Computing Equilibria in Auctions | Q1(1) | first-price variant with probabilistic allocation | 不用 revenue equivalence；直接写 value v bidder 的 expected payoff，FOC 解 symmetric bidding，再算 expected revenue。 | Lecture 7, p4-p5; Lecture 7, p9-p11 | |
| PS9 Q1 Computing Equilibria in Auctions | Q1(2) | all-pay auction equilibrium | 直接最大化 all-pay payoff；也可用 revenue equivalence 作检查，但题目要求不能用它来求 bidding strategy。 | Lecture 7, p5; Lecture 7, p18-p20 | |
| PS9 Q1 Computing Equilibria in Auctions | Q1(3) | losers-pay auction equilibrium | 写出赢时不付、输时付 bid 的 expected payoff；用 FOC 解对称递增 bid，再计算 revenue。 | Lecture 7, p5-p6; Lecture 7, p9-p11 | |
| PS9 Q2 Constructing Direct Mechanisms | Q2 | revelation principle and implementation | 固定原 auction equilibrium strategy，把报告 value 映射成原机制中的 equilibrium bid，定义同 allocation 的 direct mechanism。 | Lecture 7, p12-p18 | |
| PS9 Q3 Revenue Equivalence in Mixed Auction | Q3 | revenue equivalence and mixed first/second price | 写 bidder expected payment 为 alpha*b(v)+(1-alpha)*E[second bid conditional win]，令其等于标准 efficient auction payment。 | Lecture 7, p9-p11; Lecture 7, p18-p20 | |
| PS9 Q4 Revenue in Second-Price Auction | Q4(a) | order statistics and reserve revenue | 分解 revenue 为 reserve binds 与 second-highest binds 两项；用 uniform order statistic density 积分。 | Lecture 7, p7-p8; Lecture 7, p21-p24 | |
| PS9 Q4 Revenue in Second-Price Auction | Q4(b) | Myerson optimal reserve | 对 revenue expression 求 FOC；验证 reserve solves virtual value phi(r)=0。 | Lecture 7, p21-p24 |
反思与复盘空表
| 题目 | 题号 | 我的反思 | 下次重做策略 | 复盘日期 |
|---|---|---|---|---|
| PS1 Q1 Cournot Game with Private Costs | Q1(a) | |||
| PS1 Q1 Cournot Game with Private Costs | Q1(b) | |||
| PS1 Q1 Cournot Game with Private Costs | Q1(c) | |||
| PS1 Q2 Purification | Q2(a) | 要巧妙地构造一个 indifferent threshold | ||
| PS1 Q2 Purification | Q2(b) | 这道题的本质是在启示：本来这种 table，是存在两个 Pure NE 和一个 mixed，这道题就是让你证明当 的时候，是只有 Mixed 的。内涵的一个思想是： | ||
| PS1 Q2 Purification | Q2(c) | 当背景故事听即可，考试应该不会考 | ||
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(a) | 遇到这种问题（尤其是作为第一小问）不应该太紧张，不需要算概率，只需要分情况讨论即可（把不同的条件写出来） | ||
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(b) | 拍卖理论中的通用技巧： > 当对手使用单调策略时，获胜条件可以从”出价比较”等价转化为”类型比较”。 原因很简单：如果σ2\sigma_2 σ2严格递增，那么出价高 等同于 类型高。比较出价就等于比较类型。 | ||
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(c) | 条件期望定义。 | ||
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(d) | |||
| PS1 Q3 First-Price Sealed-Bid Auction with Common Values | Q3(e) | |||
| PS2 Q1 Global Games | Q1(a) | |||
| PS2 Q1 Global Games | Q1(b) | |||
| PS2 Q1 Global Games | Q1(c) | |||
| PS2 Q2 Disclosure Game | Q2 | 题目本身没有那么复杂，重要的是搞明白 wPBE 的三个步骤：先猜后验，然后 off-path 合法；所有的有正概率采取的行动都得过 Bayesian。 | ||
| PS3 Q1 Spence Signalling | Q1(1) | |||
| PS3 Q1 Spence Signalling | Q1(2) | |||
| PS3 Q1 Spence Signalling | Q1(3) | |||
| PS3 Q1 Spence Signalling | Q1(4) | |||
| PS3 Q2 Partial Pooling in Spence Signalling | Q2(a) | |||
| PS3 Q2 Partial Pooling in Spence Signalling | Q2(b) | |||
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(1) | |||
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(2) | |||
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(3) | |||
| PS3 Q3 Mixed Strategies in Beer and Quiche | Q3(4) | |||
| PS4 Q1 Characterizing Interval Equilibria in Cheap Talk | Q1 | |||
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(1) | |||
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(2) | |||
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(3) | |||
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(4) | |||
| PS4 Q2 Ex-Ante Payoffs in Cheap Talk Equilibria | Q2(5) | |||
| PS4 Q3 Cheap Talk with Non-Uniform State Distribution | Q3(1) | |||
| PS4 Q3 Cheap Talk with Non-Uniform State Distribution | Q3(2) | |||
| PS5 Q1 Reputation | Q1(a) | |||
| PS5 Q1 Reputation | Q1(b) | |||
| PS5 Q1 Reputation | Q1(c) | |||
| PS5 Q1 Reputation | Q1(d) | |||
| PS5 Q2 Positive Selection | Q2(a) | |||
| PS5 Q2 Positive Selection | Q2(b) | |||
| PS5 Q2 Positive Selection | Q2(c) | |||
| PS5 Q3 Certification in Adverse Selection | Q3(a) | |||
| PS5 Q3 Certification in Adverse Selection | Q3(b) | |||
| PS5 Q3 Certification in Adverse Selection | Q3(c) | |||
| PS5 Q3 Certification in Adverse Selection | Q3(d) | |||
| PS5 Q3 Certification in Adverse Selection | Q3(e) | |||
| PS6 Q1 Limited Liability | Q1(a) | |||
| PS6 Q1 Limited Liability | Q1(b) | |||
| PS6 Q2 Optimal Contract in Closed Form | Q2(a) | |||
| PS6 Q2 Optimal Contract in Closed Form | Q2(b) | |||
| PS6 Q2 Optimal Contract in Closed Form | Q2(c) | |||
| PS6 Q2 Optimal Contract in Closed Form | Q2(d) | |||
| PS6 Q2 Optimal Contract in Closed Form | Q2(e) | |||
| PS7 Q1 Uniformly Distributed Errors | Q1(a) | |||
| PS7 Q1 Uniformly Distributed Errors | Q1(b) | |||
| PS7 Q2 Simple Screening Example | Q2(a) | |||
| PS7 Q2 Simple Screening Example | Q2(b) | |||
| PS7 Q2 Simple Screening Example | Q2(c) | |||
| PS8 Q1 Taxation Principle | Q1(a) | |||
| PS8 Q1 Taxation Principle | Q1(b) | |||
| PS8 Q1 Taxation Principle | Q1(c) | |||
| PS8 Q2 Optimal Mechanism in Closed Form | Q2(a) | |||
| PS8 Q2 Optimal Mechanism in Closed Form | Q2(b) | |||
| PS9 Q1 Computing Equilibria in Auctions | Q1(1) | |||
| PS9 Q1 Computing Equilibria in Auctions | Q1(2) | |||
| PS9 Q1 Computing Equilibria in Auctions | Q1(3) | |||
| PS9 Q2 Constructing Direct Mechanisms | Q2 | |||
| PS9 Q3 Revenue Equivalence in Mixed Auction | Q3 | |||
| PS9 Q4 Revenue in Second-Price Auction | Q4(a) | |||
| PS9 Q4 Revenue in Second-Price Auction | Q4(b) |
公式自查：
条件期望定义：