... payoff) while M gives 1 irrespective of player 1’**s** strategy. Therefore, M is eliminated by mixing L and R . After eliminating M , we can further eliminate D (step 2) and L (step **3**), eventually picks up ...

20

... 複雑なゲームとはいったい何か？ 今まで扱ってきたゲーム**の**共通点 1. ゲームを利得表で表すことができた ゲームを利得表で表すことができた ゲームを利得表で表すことができた ゲームを利得表で表すことができた 2. ナッシュ均衡が（ひとつは）必ず存在した ナッシュ均衡が（ひとつは）必ず存在した ナッシュ均衡が（ひとつは）必ず存在した ナッシュ均衡が（ひとつは）必ず存在した ...

25

... M P 1 : max q≥0 p(q)q − c(q). where p(q)q is a revenue and c(q) is a cost when the output is fixed to q. Let π(q) = p(q)q − c(q) denote the revenue function. Assume that the firm’**s** objective function π(q) is ...

12

... 1. continuous at a point x 0 if, for all ε > 0, there exists δ > 0 such that d(x, x 0 ) < δ implies that d(f (x), f (x 0 )) < ε. 2. continuous if it is continuous at every point in its domain. **3**. ...

16

... Klemperer (2002), “How (not) to Run Auctions: The European 3G Telecom Auctions,” European Economic Review. Milgrom (2004) Putting Auction Theory to Work Cambridge U Press[r] ...

22

... Randomized Strategies No strategy looks to be dominated… If a player 2 randomizes L and R with 50% each, then Such mixed (randomized) strategy yields 1.5 (as an expected payoff) while M gives 1 irrespective of ...

20

... **3**. Auction (14 points) Suppose that a seller auctions one object to two buyers, = 1, 2. The buyers submit bids simultaneously, and the buyer with higher bid receives the object. The loser pays nothing while the ...

2

... 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 ...

2

... Introduction to Market Design and its Applications to School Choice.. Yosuke YASUDA.[r] ...

84

... (b) If consumer’**s** choice satis…es the weak axiom of revealed preferences, we can always construct a utility function which is consistent with such choice behav- iour. (c) If a consumer problem has a solution, then ...

2

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

1

... (a) Characterize the first-best solution. (b) Suppose that the seller cannot observe θ: θ ∈ {θ L , θ H } and Pr[θ = θ L ] = β with 0 < θ L < θ H . Set up the seller’**s** optimization problem under this ...

2

... Q = K 1 =4 L 1 =8 Then, answer the following questions. (a) In the short run, the …rm is committed to hire a …xed amount of capital K(+1), and can vary its output Q only by employing an appropriate amount of labor L . ...

3

... If the stage game has a unique NE, then for any T , the finitely repeated game has a unique SPNE: the NE of the stage game is played in every stage irrespective of the histor[r] ...

20

... 安田予想で未受賞**の**候補者たち Robert Barro (1944-, マクロ、成長理論) → イチオシ！ Elhanan Helpman (1946-, 国際貿易、成長) → 誰ともらう**の**か？ Paul Milgrom (1948-, 組織**の**経済学、オークション) → 今年は厳しい… Ariel Rubinstein (1951-, ゲーム理論) → 今年は厳しそう… ...

21

... Exist exactly one for ANY exchange problem. Always Pareto efficient and individually rational[r] ...

49

... 3(a - e)/4, is greater than aggregate quantity in the Nash equilib- rium of the Cournot game, 2(a - e)/3, so the market-clearing price is lower in the Stackelberg game.. Thus, i[r] ...

17

... A tree starts with the initial node and ends at.. terminal nodes where payoffs are specified..[r] ...

23

... A strategy in dynamic games is a complete action plan which prescribes how the player will act in each possible.. contingencies in future..[r] ...

16

... elimination of strictly dominated strategies can never be selected (with positive probability) in a mixed-strategy Nash equilibrium.[r] ...

18