# トップPDF PS5 最近の更新履歴 yyasuda's website

### PS5 最近の更新履歴 yyasuda's website

Problem Set 5: Due on July 5 Advanced Microeconomics II (Spring, 2nd, 2012) 1. Question 1 (4 points) Players 1 (proposer) and 2 (receiver) are bargaining over how to split the ice-cream of size 1. In the first stage, player 1 proposes a share {x, 1 − x} to player 2 where x ∈ [0, 1]. Player 2 can decide whether accept the offer or reject it. If player 2 accepts, then the game finishes and players get their shares. If player 2 rejects, the game move to the second stage, in which the size of the ice-cream becomes δ(∈ (0, 1)) of the original size due to melting. In the second stage, by flipping a coin, the ice-cream is randomly assigned to one of the players. Suppose each player maximizes expected size of the ice-cream that she can get. Derive a subgame perfect Nash equilibrium of this game.
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### Lec5 最近の更新履歴 yyasuda's website

elimination of strictly dominated strategies can never be selected (with positive probability) in a mixed-strategy Nash equilibrium.[r]

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### Lec8 最近の更新履歴 yyasuda's website

  A tree starts with the initial node and ends at.. terminal nodes where payoffs are specified..[r]

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### Lec2 最近の更新履歴 yyasuda's website

Prisoners’ Dilemma: Analysis     ( Silent , Silent ) looks mutually beneficial outcomes, though    Playing Confess is optimal regardless of other player’s choice!    Acting optimally ( Confess , Confess ) rends up realizing!!

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### Lec1 最近の更新履歴 yyasuda's website

Prisoners’ Dilemma: Analysis (3)    (Silent, Silent) looks mutually beneficial outcomes, though    Playing Confess is optimal regardless of other player’s choice!   Acting optimally ( Confess , Confess ) rends up realizing!!

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### Lec3 最近の更新履歴 yyasuda's website

payoff) while M gives 1 irrespective of player 1’s strategy.   Therefore, M is eliminated by mixing L and R .   After eliminating M , we can further eliminate D (step 2) and L (step 3), eventually picks up ( U , R ) as a unique outcome.

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### Lec4 最近の更新履歴 yyasuda's website

   Both the Bertrand and Cournot models are particular cases of a more general model of oligopoly competition where firms choose prices and quantities (or capacities.).   Ber[r]

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### Lec7 最近の更新履歴 yyasuda's website

Review of Lecture 5    Indifference property in mixed strategy NE.   If a player chooses more than one strategy with positive probability, she must be indifferent among such pure strategies: choosing any of them generate same expected payoff.

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### Lec10 最近の更新履歴 yyasuda's website

   If the stage game has a unique NE, then for any T , the finitely repeated game has a unique SPNE: the NE of the stage game is played in every stage irrespective of the histor[r]

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### Lec9 最近の更新履歴 yyasuda's website

3(a - e)/4, is greater than aggregate quantity in the Nash equilib- rium of the Cournot game, 2(a - e)/3, so the market-clearing price is lower in the Stackelberg game.. Thus, i[r]

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### Lec10 最近の更新履歴 yyasuda's website

   If the stage game has a unique NE, then for any T , the finitely repeated game has a unique SPNE: the NE of the stage game is played in every stage irrespective of the histor[r]

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### MarketDesign en 最近の更新履歴 yyasuda's website

  Exist exactly one for ANY exchange problem.   Always Pareto efficient and individually rational[r]

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### Nobel2015 最近の更新履歴 yyasuda's website

Paul Romer (1955-, 内生的成長理論) → 学界から消えた！？   Ben Bernanke (1953-, マクロ、金融) → FRB議長を辞めたは好材料？   Douglas Diamond (1953-, 銀行取付) → 金融は無い？   清滝信宏 (1955-, マクロ、金融) → まだ早い

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### Lec9 最近の更新履歴 yyasuda's website

3(a - e)/4, is greater than aggregate quantity in the Nash equilib- rium of the Cournot game, 2(a - e)/3, so the market-clearing price is lower in the Stackelberg game.. Thus, i[r]

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### Midterm2 最近の更新履歴 yyasuda's website

5. Mixed Strategy (20 points) Consider a patent race game in which a “weak” firm is given an endowment of 4 and a “strong” firm is given an endowment of 5, and any integral amount of the endowment could be invested in a project. That is, the weak firm has five pure strategies (invest 0, 1, 2, 3 or 4) and the strong firm has six (0, 1, 2, 3, 4 or 5). The winner of the patent race receives the return of 10. Both players are instructed that whichever player invests the most will win the race and if there is a tie, both lose: neither gets the return of 10.

### PracticeM 最近の更新履歴 yyasuda's website

(b) If consumer’s choice satis…es the weak axiom of revealed preferences, we can always construct a utility function which is consistent with such choice behav- iour. (c) If a consumer problem has a solution, then it must be unique whenever the consumer’s preference relation is convex.

### PS3 最近の更新履歴 yyasuda's website

(c) Solve for the total saving S by all types who save and the total borrowing B.. by all types who borrow.[r]

### Final14 最近の更新履歴 yyasuda's website

5. Bayesian Nash Equilibrium (12 points)  There are three different bills, \$5, \$10, and \$20. Two individuals randomly receive one  bill each. The (ex ante) probability of an individual receiving each bill is therefore 1/3.  Each  individual  knows  only  her  own  bill,  and  is  simultaneously  given  the  option  of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff (\$).
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### Midterm14 最近の更新履歴 yyasuda's website

Find (all) pure‐strategy Nash equilibrium if it exists.  iii.[r]

### Final1 最近の更新履歴 yyasuda's website

e z . The prices of the three goods are given by (p, q, 1) and the consumer’s wealth is given by ω. (a) Formulate the utility maximization problem of this consumer. (b) Note that this consumer’s preference can be expressed in the form of U (x, y, z) = V (x, y) + z. Derive V (x, y).