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... 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 ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... (a) Pure-strategy Nash equilibrium may NOT exist even if the game is …nite. (b) There MAY exist a subgame perfect Nash equilibrium which is not a Nash equilibrium. (c) Nash bargaining solution ALWAYS requires two ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... (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 ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... Axiomatic Approach (2) PAR (Pareto Efficiency) Suppose hU, di is a bargaining problem with v, v ′ ∈ U and v ′ i > v i for i = 1, 2. Then f (U, d) 6= v. The axioms SYM and PAR restrict the behavior of ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... (c) If a player randomizes pure strategies X and Y in a (mixed strategy) Nash equilibrium, she MUST be indi¤erent between choosing X and Y . 2. Monopoly (10 points) Suppose a monopoly …rm operates in two di¤erent ... 完全なドキュメントを参照

... (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 ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... Rm In essence, the PBE is a solution concept that incorporates sequential rationality and consistency of beliefs. The crucial new feature of PBE due to Kreps and Wilson (1982): Equilibrium no longer consists of ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... Suppose a seller auctions one object to two risk neutral buyers, = 1; 2. The buyers submit bids simultaneously, and the buyer with higher bid receives the object. The loser pays nothing while the winner pays a ... 完全なドキュメントを参照

... Solve the following problems in Snyder and Nicholson (11th):. 1.[r] ... 完全なドキュメントを参照

... ◮ with probability p, a consumer with wealth x will receive a times of her current wealth x ◮ with probability 1 − p she will receive b times of x. Thm Assume that the assumptions of Pratt’s Theorem holds. Then, ... 完全なドキュメントを参照

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（一般に）ナッシュ均衡は複数存在する場合がある
プレイヤー全員にとってあるナッシュ均衡よりも別のナッシュ 均衡の方が望ましい場合もある
良い均衡（Mac, Mac）ではなく悪い均衡（ Win , Win ）が選 ばれてしまう危険性がある ... 完全なドキュメントを参照

... How to Measure Welfare Change | 厚生の変化をどうはかるか？ When the economic environment or market outcome changes, a consumer may be made better off ( 改善 ) or worse off ( 悪化 ). Economists often want to measure how consumers ... 完全なドキュメントを参照