Micro Economics Chap.7&8 7章 時間を通じたゲームと戦略の信頼性 1. Resolution of Failed Financial（銀行の破綻処理） 2. Subgame Perfect Equilibrium (部分ゲーム完全均衡) 3. Application to The Oligopoly (寡占への応用) 4. Commitment (コミットメント) 5. Long-term Relations and Cooperation (長期的関係と協調) 8章 保険とモラル・ハザード 1. Risk Sharing and insurance (効率的な危険分担と保険の役割) 2. Moral Hazard and That Counterplan (モラル・ハザードとその対策) 福田研究室ゼミ 6.17 水口 正教 第7章 時間を通じたゲームと 戦略の信頼性 1. Resolution of Failed Financial 銀行の破綻処理 Tree of game ゲームの木；展開型表現 ミクロ経済学の力 P.363 図7.4 The action of a player who moves first depends what will happen in the future It is necessary to solve a game from future 3 (Action plan with the condition：条件付き行動計画) 1. Resolution of Failed Financial 銀行の破綻処理 Supposing that all player choose an action at the same time ミクロ経済学の力 P.361 表7.1 ② is claptrap はったり ① is more realistic (Subgame perfect equilibrium：部分ゲーム完全均衡) 4 2. Subgame Perfect Equilibrium 部分ゲーム完全均衡 Information set of the player：プレーヤーの情報集合 ミクロ経済学の力 P.364 図7.5 ミクロ経済学の力 P.365 図7.6 player ∶ 𝑖 , action ∶ 𝑥𝑖 𝑡 𝑥𝑖 𝑡 = 𝑠𝑖 𝑖が𝑡時点までに観察したものすべて 𝐹 = 𝑠2 𝐹 , 𝑆 = 𝑠2 (𝑆) 5 2. Subgame Perfect Equilibrium 部分ゲーム完全均衡 Subgame：If all the players moving form now watches all having happened for a past, it called “subgame” from there to finished the game ミクロ経済学の力 P.369 図7.9 ミクロ経済学の力 P.370 図7.10 6 2. Subgame Perfect Equilibrium 部分ゲーム完全均衡 Subgame Perfect Equilibrium : a refinement of a Nash equilibrium used in dynamic games ミクロ経済学の力 P.372 図7.11 7 2. Subgame Perfect Equilibrium 部分ゲーム完全均衡 e.g. Battle of sex (Football of Shopping) ①Find the nash equilibrium of subgame ミクロ経済学の力 P.372 図7.12 ②Find the whole equilibrium ミクロ経済学の力 P.373 図7.13 8 3. Application to The Oligopoly 寡占への応用 Supply curve: P = 𝑎 − 𝑏𝑄 Company: 𝑖 = 1,2 Marginal cost: MC1 = 𝑀𝐶2 = 𝑐 Cournot (Q) or Bertrand(P) two companies move through time (Stackelberg Model) • First, company1(leader) chose quantity 𝑞1 • Next, company2(follower) chose quantity 𝑞2 Step 1 Solve the subgame after leader decided the strategy 𝑞2 = 𝑅2 (𝑞1 ) Step 2 Leader decides the strategy based on step1 9 3. Application to The Oligopoly 寡占への応用 Supply curve: P = 𝑎 − 𝑏𝑄 Company: 𝑖 = 1,2 Marginal cost: MC1 = 𝑀𝐶2 = 𝑐 Let’s calculate concretely! Step 1 Profit of company 2 𝜋2 = 𝑎 − 𝑏 𝑞1 + 𝑞2 − 𝑐 𝑞2 𝜕𝜋2 = 𝑎 − 𝑏𝑞1 − 2𝑏𝑞2 − 𝑐 = 0 𝜕𝑞2 solve this equation 𝑎−𝑐 1 𝑞2 = 𝑅2 𝑞1 = 2𝑏 − 2 𝑞1 Step 2 Profit of company 1 𝜋1 𝑞1 , 𝑅2 𝑞1 = 𝑎 − 𝑏 𝑞1 + 𝑅2 𝑞1 𝑎−𝑐 𝑏 = − 𝑞1 𝑞1 2 2 𝑑𝜋1 𝑎 − 𝑐 = − 𝑏𝑞1 = 0 𝑑𝑞1 2 − 𝑐 𝑞1 𝑎−𝑐 2𝑏 𝑎−𝑐 𝑞2∗ = 𝑅2 𝑞1 = 4𝑏 (Stackelberg’s solution) 𝑞1∗ = 10 3. Application to The Oligopoly 寡占への応用 Let’s illustrate! Supply curve: P = 𝑎 − 𝑏𝑄 Company: 𝑖 = 1,2 Marginal cost: MC1 = 𝑀𝐶2 = 𝑐 Step 1 ミクロ経済学の力 P.377 図7.15 ミクロ経済学の力 P.379 図7.17 Equal profit curve Stackelberg’s solution Step 2 11 3. Application to The Oligopoly 寡占への応用 Let’s illustrate! Supply curve: P = 𝑎 − 𝑏𝑄 Company: 𝑖 = 1,2 Marginal cost: MC1 = 𝑀𝐶2 = 𝑐 Leaders quantity → increase Leaders profit → increase ミクロ経済学の力 P.379 図7.18 Stackelberg’s solution → leader cannot change the strategy Cournot ‘s solution → leader(company1) can change Make getting only a specific action may be advantageous Cournot ‘s solution and Stackelberg’s solution (commit to specific production) 12 4. Commitment コミットメント When a financial panic is caused, it adversely affects the society Government will relieve financial organs Commitment Small profit ミクロ経済学の力 P.358 図7.1 large profit 13 4. Commitment コミットメント • Counterterrorism(テロ対策) Commitment 14 4. Commitment コミットメント • Lowest price guarantee(最低価格保証) Commitment （価格を下げない） 15 5. Long-term Relations and Cooperation 長期的関係と協調 Bertrand’s model? (𝑀𝐶1 = 𝑀𝐶2 = 𝑐) Consider to be a repeated game same player plays same “stage game” repeatedly 16 5. Long-term Relations and Cooperation 長期的関係と協調 repeated game set a price in p(>c) for the beginning make a price c forever if anyone set a price p’ ミクロ経済学の力 P.395 表7.5 Trigger strategy 17 5. Long-term Relations and Cooperation 長期的関係と協調 repeated game Trigger strategy ミクロ経済学の力 P.395 表7.5 Does they profit when they betray it? Discount factor 割引因子 : 𝛿 (0 < 𝛿 < 1) Gain of player 𝑖 𝜋𝑖 0 + 𝜋 𝑖 1 𝛿 + 𝜋𝑖 2 𝛿 2 + ⋯ Gain of player 𝑖 when 𝑖 denounce 2𝜋 ∗ − 𝜋 ∗ = 𝜋 ∗ Loss of player 𝑖 when 𝑖 denounce X = 𝜋 ∗𝛿 + 𝜋 ∗𝛿 2 + ⋯ = 𝜋 ∗𝛿 + 𝛿 𝜋 ∗𝛿 + 𝜋 ∗𝛿 2 + ⋯ = 𝜋 ∗ 𝛿 + 𝛿𝑋 𝛿 𝑋= 𝜋∗ 1−𝛿 What kind of situation that they denounce? 𝛿 1 𝜋∗ ≥ 𝜋∗ ⟺ 𝛿 ≤ 1−𝛿 2 Structure 18 of the cartel 第8章 保険とモラル・ハザード 1. Risk Sharing and Insurance 効率的な危険分担と保険の役割 Review of last week：expected utility model(期待効用モデル) ミクロ経済学の力 P.401 図8.1 20 1. Risk Sharing and Insurance 効率的な危険分担と保険の役割 Probability p which happen of the earthquake Income x1 (=¥0) at that time Income x2 (=¥100) at the other time expected utility 21 1. Risk Sharing and Insurance 効率的な危険分担と保険の役割 Probability p which happen of the earthquake Income x1 (=¥0) at that time Income x2 (=¥100) at the other time ¥100 or ¥0 ミクロ経済学の力 P.401 図8.2 ¥100(１－p) Risk sharing (Pareto efficiency) 22 1. Risk Sharing and Insurance 効率的な危険分担と保険の役割 insurance initial sum ミクロ経済学の力 P.401 図8.2 insurance money risk 23 2. Moral Hazard and That Counterplan モラルハザードとその対策 ① ③ result of action request ミクロ経済学の力 P.404 図8.3 ② or ミクロ経済学の力 P.404 図8.3 ↑ Moral hazard 24 2. Moral Hazard and That Counterplan モラルハザードとその対策 Counterplan of moral hazard → Theory of the agency Principal : risk neutral Agent : risk avert ミクロ経済学の力 P.407 図8.4 ①Principal gives the enough reward for an agent (Participation condition) ② links the reward and the result (Incentive condition) 25 2. Moral Hazard and That Counterplan モラルハザードとその対策 Theory of the agency result 𝑦 𝑝 ミクロ経済学の力 P.404 図8.3 1−𝑝 𝑦 ①Principal gives the enough reward for an agent ② links the reward and the result reward 𝑤 𝑤 * Expectation of the profit of principal ① Participation condition result 𝑦 𝑝′ ミクロ経済学の力 P.404 図8.3 1 − 𝑝′ 𝑦 Cost when agent do it seriously Gain when agent works in other companies ② Incentive condition Principal maximize * Under the condition ① and ② 26 2. Moral Hazard and That Counterplan モラルハザードとその対策 * = change indifference curve of principal ミクロ経済学の力 P.409 図8.5 27 2. Moral Hazard and That Counterplan モラルハザードとその対策 indifference curve of agent ミクロ経済学の力 P.410 図8.6 Utility of agent （①） ミクロ経済学の力 P.401 図8.1 differentiate in 𝑤 ← The slope of the rate curve 28 2. Moral Hazard and That Counterplan モラルハザードとその対策 ② ミクロ経済学の力 P.413 図8.9 ミクロ経済学の力 P.412 図8.8 Agent has no risk, Effective risk sharing 29
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