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... Using this minimax theorem, answer the following questions. (b) Show that Nash equilibria are interchangeable; if and are two Nash equilibria, then and are also Nash equilibria. (c) Show that each player’s payo¤ ... 完全なドキュメントを参照

... (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 ... 完全なドキュメントを参照

... (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 ... 完全なドキュメントを参照

... 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 ... 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

... 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 ... 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

... 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

... 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

... 1 It may stay out (O), 2 prepare itself for combat and enter (“Ready” = R), 3 or enter without making preparations (“Unready” = U ). Preparation is costly but reduces the loss from a fight. The incumbent may ... 完全なドキュメントを参照

... 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 ... 完全なドキュメントを参照

... 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 ... 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

... 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

... 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

... 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 ... 完全なドキュメントを参照

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（お互いの行動に関する）「正しい予想の共有＋合理性」 によってナッシュ均衡は実現する！ ... 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

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