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 ( U , R ) as a unique outcome.

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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

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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 convex and differentiable. Then, the first order condition is:

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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**. uniformly continuous if, for all ε > 0, there exists δ > 0 such

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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]

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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 player 1’**s** strategy.

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

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(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 it must be unique whenever the consumer’**s** preference relation is convex.

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

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(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 asymmetric
information structure.

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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 . Derive the …rm’**s** short-run total, average, and marginal cost functions. (b) In the long run, the …rm can vary both capital and labor. Derive the …rm’**s**

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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]

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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…

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

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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]

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

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

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

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