トップPDF PS2 2and3 最近の更新履歴 yyasuda's website

Players 1 (proposer) and 2 (receiver) are bargaining over how to split the ice-cream of size 1. In the first stage, player 1 proposes a share {x, 1 − x} to player 2 where x ∈ [0, 1] is player 1’s own share. Player 2 can decide whether accept the offer or reject it. If player 2 accepts, then the game finishes and players get their shares. If player 2 rejects, the game move to the second stage, in which the size of the ice-cream becomes δ(∈ (0, 1)) of the original size due to melting. In the second stage, by flipping a coin, the ice-cream is randomly assigned to one of the players. Suppose each player maximizes expected size of the ice-cream that she can get. Derive a subgame perfect Nash equilibrium of this game.

Players 1 (proposer) and 2 (receiver) are bargaining over how to split the ice-cream of size 1. In the first stage, player 1 proposes a share {x, 1 − x} to player 2 where x ∈ [0, 1] is player 1’s own share. Player 2 can decide whether accept the offer or reject it. If player 2 accepts, then the game finishes and players get their shares. If player 2 rejects, the game move to the second stage, in which the size of the ice-cream becomes δ(∈ (0, 1)) of the original size due to melting. In the second stage, by flipping a coin, the ice-cream is randomly assigned to one of the players. Suppose each player maximizes expected size of the ice-cream that she can get. Derive a subgame perfect Nash equilibrium of this game.

Eco 601E: Advanced Microeconomics II (Fall, 2nd, 2013) Final Exam: January 28 1. Dynamic Game (24 points) Consider the following two-person dynamic game. In the first period, game A is played; after observing each player’s actions, they play game B in the second period. Assume that the payoffs are simply the sum of the payoffs of two games (i.e., there is no discounting).

(c) Any finite game has at least one Nash equilibrium in pure strategies. 2. Expected Utility (16 points) Suppose that an individual can either exert effort or not. Her initial wealth is $100 and the cost of exerting effort is c. Her probability of facing a loss $75 (that is, her wealth becomes $25) is 1

(e) The social welfare function introduced by Arrow is to derive social UTILITY by adding up individual utilities. 2. Externalities (25 points) Consider a one-consumer, one-firm economy (or equiv- alently an economy with many identical consumers and firms.) There are two private commodities. The firm also produces a level of pollution b. The produc- tion set of the firm is the convex set γ = {(y 1 , y 2 , b | G(y 1 , y 2 , b ) ≤ 0)}, where G

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 the solution on single bargaining problems, while INV and IIA require the solution to exhibit some consistency across bargaining problems.

A good is called normal (resp. inferior) if consumption of it increases (resp. declines) as income increases, holding prices constant.. Show the following claims.[r]

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

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¤ is the same in every Nash equilibrium.

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

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 >

2. Duopoly (15 points) Consider a duopoly game in which two firms, denoted by Firm 1 and Firm 2, simultaneously and independently select their own prices, p 1 and p 2 , respectively. The firms’ products are differentiated. After the prices are set, consumers demand A − p i +

(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.

Suppose a government auctions one block of radio spectrum to two risk neutral 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:

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 weighted average of the two bids b+b 2 0 where b is the winner’s bid, b 0 is the loser’s bid. Assume that the valuation of the

(d) Now suppose that the …rms interact inde…nitely through time. They discount future pro…ts at a discount factor . For what value of is there an equilibrium where …rms follow the “trigger strategies”, i.e., they produce cartel output as long as the other …rm has always produced cartel output and otherwise they produce Cournot Nash output?

合理的な豚：分析
子豚には最適戦略（支配戦略）が存在する！
大豚の行動によらず「 待つ 」のが常に最適
子豚が合理的ならば絶対にスイッチを押さない
子豚の「 スイッチを押す 」は可能性から消去される

Dual Problem - Theory | 双対問題 - 理論 (1) Applying the duality idea to the consumer problem, we can establish the close relationship between the indirect utility and expenditure functions, and between the Marshallian and Hicksian demand functions.

Problem Set 3: Due on July 17 Advanced Microeconomics II (Spring, 2nd, 2013) 1. Question 1 (4 points) Consider the following labor market signaling game. There are two types of worker. Type 1 worker has a marginal value product of 1 and type 2 worker has a marginal value product of 2. The cost of signal z for type 1 is C 1 (z) = z and for type 2 is C 2 (z) = (1 − c)z. The worker is type 1 with probability

Players 1 (proposer) and 2 (receiver) are bargaining over how to split the ice-cream of size 1. In the first stage, player 1 proposes a share {x, 1 − x} to player 2 where x ∈ [0, 1] is player 1’s own share. Player 2 can decide whether accept the offer or reject it. If player 2 accepts, then the game finishes and players get their shares. If player 2 rejects, the game move to the second stage, in which the size of the ice-cream becomes δ(∈ (0, 1)) of the original size due to melting. In the second stage, by flipping a coin, the ice-cream is randomly assigned to one of the players. Suppose each player maximizes expected size of the ice-cream that she can get. Derive a subgame perfect Nash equilibrium of this game.