# トップPDF Slide2 最近の更新履歴 yyasuda's website ### Slide2 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]

16 さらに読み込む ### geo slide06 最近の更新履歴 yyasuda's website

Outcome of JRMP May Violate Weak Stability The same example as before: There are two hospitals h 1 , h 2 in one region with regional cap 10. Each hospital has a capacity of 10 and a target capacity of 5. There are 10 doctors, d 1 , . . . , d 10 such that

24 さらに読み込む ### Final2 13 最近の更新履歴 yyasuda's website

is strictly increasing in its first two arguments and strictly decreasing in b. Thus by increasing pollution, the firm can produce more output (or use less input). The consumer has a concave utility function U (y 1 , y 2 , b ) that is also increasing in its first two arguments and decreasing in b. ### 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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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, ### Midterm2 10 最近の更新履歴 yyasuda's website

3. Nash Equilibrium (16 points) Monica and Nancy have formed a business partnership. Each partner must make her e¤ort decision without knowing what e¤ort decision the other player has made. Let m be the amount of e¤ort chosen by Monica and n be the amount of e¤ort chosen by Nancy. The joint pro…ts are given by 4m + 4n + mn, and two partners split these pro…ts equally. However, they must each separately incur the costs of their own e¤ort, which is a quadratic function of the amount of e¤ort, i.e., m 2 and ### Final2 14 最近の更新履歴 yyasuda's website

4. Auctions (30 points) Suppose that the government auctions one block of radio spectrum to two risk neu- tral mobile phone companies, i = 1, 2. The companies submit bids simultaneously, and the company with higher bid receives a spectrum block. The loser pays nothing while the winner pays a weighted average of the two bids: ### Midterm2 14 最近の更新履歴 yyasuda's website

Three firms (1, 2 and 3) put three items on the market and can advertise these products either on morning (= M ) or evening TV (= E). A firm advertises exactly once per day. If more than one firm advertises at the same time, their profits become 0. If exactly one firm advertises in the morning, its profit is 1; if exactly one firm advertises in the evening, its profit is 2. Firms must make their daily advertising decisions simultaneously. ### Lec2 15 最近の更新履歴 yyasuda's website

However, it is difficult to assess how reasonable some axioms are without having in mind a specific bargaining procedure. In particular, IIA and PAR are hard to defend in the abstract. Unless we can find a sensible strategic model that has an equilibrium corresponding to the Nash solution, the appeal of Nash’s axioms is in doubt.

11 さらに読み込む ### Lec2 14 最近の更新履歴 yyasuda's website

where u i (x, θ i ) is the money-equivalent value of alternative x ∈ X. This assumes the case of private values in which player i’s payoff does not depend directly on other players’ types. If it does, then it is called common values case. The outcome (of the mechanism) is described by

16 さらに読み込む ### Lec2 13 最近の更新履歴 yyasuda's website

R i (or % i ) An individual i’s preference relation on X (an binary relation satisfying completeness and transitivity. → Let P i (or ≻i) and I i (or ∼i) be the associated relations of strict individual preference and indifference, respectively.

13 さらに読み込む ### Lec2 11 最近の更新履歴 yyasuda's website

β(x i ) = c + θx i . (1) Now suppose that player 2 follows the above equilibrium strategy, and we shall check whether player 1 has an incentive to choose the same linear strategy (1). Player 1’s optimization problem, given she received a valuation x 1 , is

15 さらに読み込む ### 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

12 さらに読み込む ### 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. ### Final2 10 最近の更新履歴 yyasuda's website

object for each buyer is independently and uniformly distributed between 0 and 1. (a) Suppose that buyer 2 takes a linear strategy, b 2 = v 2 . Then, derive the probability such that buyer 1 wins as a function of b 1 . (b) Solve a Bayesian Nash equilibrium. ### PS2 2 最近の更新履歴 yyasuda's website

(a) Find a Bayesian Nash equilibrium of the game in pure strategies in which each player i accepts an exchange if and only if the value v i does not exceed some threshold θ i (b) How would your answer to (a) change if the value of player i’s house to the other player j becomes 5 ### PQ2 2 最近の更新履歴 yyasuda's website

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