トップPDF Midterm2 最近の更新履歴 yyasuda's website

Midterm2 最近の更新履歴  yyasuda's website

Midterm2 最近の更新履歴 yyasuda's website

(a) If an agent is risk averse, her risk premium is ALWAYS positive. (b) When every player has a (strictly) dominant strategy, the strategy profile that consists of each player’s dominant strategy MUST be a Nash equilibrium. (c) If there are two Nash equilibria in pure-strategy, they can ALWAYS be Pareto

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Final2 12 最近の更新履歴  yyasuda's website

Final2 12 最近の更新履歴 yyasuda's website

(d) Zermelo’s theorem assures that the first mover has a winning strategy in ANY perfect information game with strictly opposite interests. (e) The weak perfect Bayesian equilibrium puts NO restriction on beliefs at the information sets that are not reached in equilibrium.

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

Midterm2 10 最近の更新履歴 yyasuda's website

(d) What is the Nash equilibrium of this game? 4. Mixed Strategy (15 points) Three …rms (1, 2 and 3) put three items on the market and can advertise these products either on morning (= M ) or evening TV (= E). A …rm advertises exactly once per day. If more than one …rm advertises at the same time, their pro…ts become 0. If exactly one …rm advertises in the morning, its pro…t is 1; if exactly one …rm advertises in the evening, its pro…t is 2. Firms must make their daily advertising decisions simultaneously.

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Final2 11 最近の更新履歴  yyasuda's website

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 13 最近の更新履歴  yyasuda's website

Final2 13 最近の更新履歴 yyasuda's website

(c) Confirm that by choosing the tax t appropriately, the socially optimal level of pollution is produced. (d) Add a second firm with a different production function. Now the consumers observe a pollution level b = b 1 + b 2 . Show that the social optimum can still

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Final2 10 最近の更新履歴  yyasuda's website

Final2 10 最近の更新履歴 yyasuda's website

Consider the following two-person dynamic game. In the …rst period, game A is played; after observing each player’s actions, they play game B in the second period. Assume that the payo¤s are simply the sum of the payo¤s of two games (i.e., there is no discounting).

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Final2 14 最近の更新履歴  yyasuda's website

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:

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Midterm2 14 最近の更新履歴  yyasuda's website

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.

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Lec2 最近の更新履歴  yyasuda's website

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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Lec2 12 最近の更新履歴  yyasuda's website

Lec2 12 最近の更新履歴 yyasuda's website

That is, given that the incumbent’s information set is reached, choosing A is clearly optimal irrespective of her belief over nodes. → Choosing F looks non-credible. SPNE cannot eliminate this since there is no proper subgame. Weak perfect Bayesian equilibrium (explain in detail later) is enough to exclude (O, F ) in this case.

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Lec2 10 最近の更新履歴  yyasuda's website

Lec2 10 最近の更新履歴 yyasuda's website

A belief about other players’ types is a conditional probability distribution of other players’ types given the player’s knowledge of her own type p i (t −i |t i ). When nature reveals t i to player i, she can compute the belief p i (t −i |t i ) using Bayes’ rule:

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Lec2 11 最近の更新履歴  yyasuda's website

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 15 最近の更新履歴  yyasuda's website

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.

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Lec2 13 最近の更新履歴  yyasuda's website

Lec2 13 最近の更新履歴 yyasuda's website

Proof Sketch (2): Existence of Pivotal Voter Lemma 3 (Existence of Pivotal Voter) There is a voter n ∗ = n(b) who is extremely pivotal in the sense that by changing his vote at some profile he can move b from the very bottom of the social ranking to the very top.

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PS2 1 最近の更新履歴  yyasuda's website

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

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Final2 08 最近の更新履歴  yyasuda's website

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.

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Micro2 最近の更新履歴  yyasuda's website

Micro2 最近の更新履歴 yyasuda's website

Dual Problem - Theory | 双対問題 - 理論 (3) Thm Suppose the consumer’s preference is continuous, monotone and strictly convex. Then, we have the following relations between the Hicksian and Marshallian demand functions for p ≫ 0, ω ≥ 0 and u ∈ R, and i = 1, 2, ..., n:

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PS2 最近の更新履歴  yyasuda's website

PS2 最近の更新履歴 yyasuda's website

Let w = (w 1 , w 2 , w 3 , w 4 ) ≫ 0 be factor prices and y be an (target) output. (a) Does the production function exhibit increasing, constant or decreasing returns to scale? Explain. (b) Calculate the conditional input demand function for factors 1 and 2. (c) Suppose w 3 >

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Lec2 最近の更新履歴  yyasuda's website

Lec2 最近の更新履歴 yyasuda's website

 すべてプレーヤーに支配戦略が無いゲームでも解け る場合がある  「支配される戦略逐次消去」(後述)  (お互い行動に関する)「正しい予想共有+合理性」 によってナッシュ均衡は実現する!

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PQ2 最近の更新履歴  yyasuda's website

PQ2 最近の更新履歴 yyasuda's website

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

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