# トップPDF EX2 2 最近の更新履歴 yyasuda's website

### EX2 2 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

### EX2 2 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

### Final2 10 最近の更新履歴 yyasuda's website

(b) Revenue equivalence theorem claims that the equilibrium bidding strategy under the …rst-price auction is ALWAYS identical to the one under the second- price auction. (c) EVERY perfect Bayesian equilibrium is a weak perfect Bayesian equilibrium. 2. Dynamic Game (14 points)

### PS2 1 最近の更新履歴 yyasuda's website

Explain. (b) Show that any risk averse decision maker whose preference satisfies indepen- dence axiom must prefer L 2 to L 3 . 3. Question 3 (4 points) Suppose a monopolist with constant marginal costs prac- tices third-degree price discrimination. Group A’s elasticity of demand is ǫ A and

### Final2 08 最近の更新履歴 yyasuda's website

b + (1 )b 0 where b is the winner’s bid, b 0 is the loser’s bid, and is some constant satisfying 0 1. (In case of ties, each company wins with equal probability.) Assume the valuation of the spectrum block for each company is independently and uniformly distributed between 0 and 1.

### Midterm2 10 最近の更新履歴 yyasuda's website

(a) Derive each partner’s payo¤ function. (b) Derive each partner’s best reply function and graphically draw them in a …gure. (Taking m in the horizontal axis and n in the vertical axis.) (c) Is this game strategic complementarity, strategic substitution, or neither of them? Explain why.

### Lec2 13 最近の更新履歴 yyasuda's website

Arrow’s Requirements of the SWF (1) Unrestricted Domain (UD) The domain of f must include all possible combinations of individual preference relations on X. Weak Pareto Principle (WP) For any pair of alternatives x and y in X, if xP i y for all i, then xP y.

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### Final2 11 最近の更新履歴 yyasuda's website

5. Bayesian Game (20 points) There are 10 envelopes and each of them contains a number 1 through 10. That is, one envelope contains 1, another envelope contains 2, and so on; these numbers cannot be observable from outside. Suppose there are two individuals. Each of them randomly receives one envelope and observes the number inside of her/his own envelope. Then, they are given an option to exchange the envelope to the other person; exchange occurs if and only if both individuals wish to exchange. Finally, individuals receive prize (\$) equal to the number, i.e., she receives \$X if the number is X. Assume that both individuals are risk-neutral so that they maximize expected value of prizes.
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### Final2 12 最近の更新履歴 yyasuda's website

3. Auction (9 points) Consider a “common-value auction” with two players, where the value of the object being auctioned is identical for both players. Call this value V and suppose that V = v 1 + v 2 , where v i is independently and uniformly distributed between 0 and 1,

### Final2 13 最近の更新履歴 yyasuda's website

Hint: Your answers in (a) – (c) may change depending on the value of θ. 4. Duopoly (20 points) Consider a duopoly game in which two firms, denoted by firm 1 and firm 2, simul- taneously and independently select their own price, p 1 and p 2 . The firms’ products are differentiated. After the prices are set, consumers demand 24 − p i +

### Lec2 2 最近の更新履歴 yyasuda's website

Proof of Pratt’s Theorem (1) Sketch of the Proof. To establish (i) ⇔ (iii), it is enough to show that P is positively related to r. Let ε be a “small” random variable with expectation of zero, i.e., E(ε) = 0. The risk premium P (ε) (at initial wealth x) is defined by

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### Lec2 10 最近の更新履歴 yyasuda's website

Rm Each of these utility functions measures the change in the player’s utility. If there is no trade, then there is no change in utility. It would make no difference to define, say, the seller’s utility to be p if there is trade at price p and v s if there is no trade.

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### Lec2 7 最近の更新履歴 yyasuda's website

1 2 . A leader never becomes worse off since she could have achieved Cournot profit level in the Stackelberg game simply by choosing the Cournot output: a gain from commitment. A follower does become worse off although he has more information in the Stackelberg game than in the Cournot game, i.e., the rivals output.

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### Lec2 9 最近の更新履歴 yyasuda's website

Rm Since every subgame of an infinitely repeated game is identical to the game as a whole, we have to consider only two types of subgames: (i) subgame in which all the outcomes of earlier stages have been (C1, C2), and (ii) subgames in which the outcome of at least one earlier stage differs from (C1, C2).

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### Lec2 11 最近の更新履歴 yyasuda's website

First-Price: General Model (1) Consider a first-price auction with n bidders in which all the conditions in the previous theorem are satisfied. Assume that bidders play a symmetric equilibrium, β(x). Given some bidding strategy b, a bidder’s expected payoff becomes

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### Lec2 12 最近の更新履歴 yyasuda's website

1 Nature draws a type t i for the Sender from a set of feasible types T = {t1 , ..., t I} according to a probability distribution p(ti), where p(ti) > 0 for every i and p(t 1 ) + · · · + p(tn) = 1. 2 Sender observes ti and then chooses a message mj from a set

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### PS2 最近の更新履歴 yyasuda's website

Problem Set 2: Posted on November 4 Advanced Microeconomics I (Fall, 1st, 2014) 1. Question 1 (7 points) A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree 1. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.

### PQ2 最近の更新履歴 yyasuda's website

Solve the following problems in Snyder and Nicholson (11th):. 1.[r]

### PS2 最近の更新履歴 yyasuda's website

Problem Set 2: Due on May 14 Advanced Microeconomics I (Spring, 1st, 2013) 1. Question 1 (6 points) (a) Suppose the utility function is continuous and strictly increasing. Then, show that the associated indirect utility function v(p, ω) is quasi-convex in (p, ω). (b) Show that the (minimum) expenditure function e(p, u) is concave in p.

### Lec2 最近の更新履歴 yyasuda's website

Open Set and Closed Set (2) Boundary and interior ◮ A point x is called a boundary point of a set S in R n if every ε-ball centered at x contains points in S as well as points not in S. The set of all boundary points of a set S is called boundary, and is denoted ∂S .

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