メモリー 3CHに D 0 ∼ D 25 にセットされたデータを書き込みます。セットされたデータ**の**周波数が
同時に D D S **の**出力周波数となります。 周波数データ**の**計算方法は、項目 10 を参照してください。
コマンドＦ メモリー 4CHに 26 ビット**の**周波数データを書き込みと同時に D D S **の**出力する
メモリー 4CHに D 0 ∼ D 25 にセットされたデータを書き込みます。セットされたデータ**の**周波数が

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ユーザが行う唯一**の**貢献は、いくつか**の**コネクタを溶接すること、トロイドを作るこ と、いくつか**の**リードをはんだ付けすること、
レギュレータと最終トランジスタ**の**ペア、巻線トランス... うわー、あなたはもはや 私は **2** 枚**の**プリント基板が付属している最初**の** **2** 枚を持っていました。

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Notes
1. Please consult the most recently issued data sheet before initiating or completing a design.
**2**. The product status of the device(**s**) described in this data sheet may have changed since this data sheet was published. The latest information is available on the Internet at URL http://www.semiconductors.philips.com. 3. For data sheets describing multiple type numbers, the highest-level product status determines the data sheet status.

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RED BLUE GRAY BLACK WHITE GREEN BROWN YELLOW Code.[r]

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(a) Write the payoff functions π 1 and π **2** (as a function of p 1 and p **2** ).
(b) Derive the best response functions and solve the pure-strategy Nash equilib- rium of this game.
(c) Derive the prices (p 1 , p **2** ) that maximize joint-profit, i.e., π 1 + π **2** .

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 from outside. Suppose there are two individuals. Each of them randomly receives one envelope and observes the number inside of her/his own envelope. Then, they are given an option to exchange the envelope to the other person; exchange occurs if and only if both individuals wish to exchange. Finally, individuals receive prize ($) equal to the number, i.e., she receives $X if the number is X. Assume that both individuals are risk-neutral so that they maximize expected value of prizes.

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(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 + b **2** . Show that the social optimum can still

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.

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 higher bid receives a spectrum block. The loser pays nothing while the winner pays a weighted average of the two bids:

3. Nash Equilibrium (16 points)
Monica and Nancy have formed a business partnership. Each partner must make her e¤ort decision without knowing what e¤ort decision the other player has made. Let m be the amount of e¤ort chosen by Monica and n be the amount of e¤ort chosen by Nancy. The joint pro…ts are given by 4m + 4n + mn, and two partners split these pro…ts equally. However, they must each separately incur the costs of their own e¤ort, which is a quadratic function of the amount of e¤ort, i.e., m **2** and

4. Simultaneous Game (20 points, moderate)
Suppose three cafe chain companies, i = 1; **2**; 3, are considering to open new shops near the Roppongi cross (Each company opens at most one shop). They make the decision independently and simultaneously. A company receives 0 pro…t if it does not open a shop. If opens, then each …rm’**s** pro…ts depend on the number of shops which are given as follows:

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 third-degree price discrimination. Group A’**s** elasticity of demand is ǫ A and

Each player’**s** strategy specifies optimal actions given her beliefs and the strategies of the other players, and
The beliefs are consistent with Bayes’ rule wherever possible. If (4) is not required, the equilibrium concept is called weak perfect Bayesian equilibrium (weak PBE).

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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 very bottom of the social ranking to the very top.

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However, it is difficult to assess how reasonable some axioms are without having in mind a specific bargaining procedure. In particular, IIA and PAR are hard to defend in the abstract. Unless we can find a sensible strategic model that has an equilibrium corresponding to the Nash solution, the appeal of Nash’**s** axioms is in doubt.

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object for each buyer is independently and uniformly distributed between 0 and 1. (a) Suppose that buyer **2** takes a linear strategy, b **2** = v **2** . Then, derive the
probability such that buyer 1 wins as a function of b 1 .
(b) Solve a Bayesian Nash equilibrium.

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.

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Constant Absolute Risk Aversion
Def We say that preference relation % exhibits invariance to
wealth if (x + p 1 ) % (x + p **2** ) is true or false independent of x.
Thm If u is a vNM continuous utility function representing preferences that are monotonic and exhibit both risk aversion and invariance to wealth, then u must be exponential,

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Edgeworth Box | エッジワース・ボックス
The most useful example of an exchange economy is one in which there are two people and two goods. This economy’**s** set of allocations can be illustrated in an Edgeworth box ( エッジワース・ボックス ) diagram.

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