(c) Solve for the total saving S by all types who save and the total borrowing B.. by all types who borrow.[r]

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Problem Set **3**: Due on May 28
Advanced Microeconomics I (Spring, 1st, 2013) 1. Question 1 (5 points)
A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree 1. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.

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Problem Set **3**: Due on May 24
Advanced Microeconomics I (Spring, 1st, 2012) 1. Question 1 (4 points)
A real-valued function f (x) is called homothetic if f (x) = g(h(x)) where g : R → R is a strictly increasing function and h is a real-valued function which is homo- geneous of degree 1. Suppose that preferences can be represented by a homothetic utility function. Then, prove the following statements.

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Ann and Bob are in an Italian restaurant, and the owner offers them a free **3**- slice pizza under the following condition. Ann and Bob must simultaneously and independently announce how many slice(**s**) she/he would like: Let a and b be the amount of pizza requested by Ann and Bob, respectively (you can assume that a and b are integer numbers between 1 and **3**). If a + b ≤ **3**, then each player gets her/his requested demands (and the owner eats any leftover slices). If a + b > **3**, then both players get nothing. Assume that each players payoff is equal to the number of slices of pizza; that is, the more the better.

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(5) Suppose that this game is played finitely many times, say T (≥ 2) times. De- rive the subgame perfect Nash equilibrium of such a finitely repeated game. Assume that payoff of each player is sum of each period payoff.
(6) Now suppose that the game is played infinitely many times: payoff of each player is discounted sum of each period payoff with some discount factor δ ∈ (0, 1). Assume specifically that A = 16, c = 8. Then, derive the condition under which the trigger strategy sustains the joint-profit maximizing prices you derived in (**3**) (as a subgame perfect Nash equilibrium).

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

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

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

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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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A set S in R n is called compact if it is closed and bounded.
Theorem **3** (Weierstrass, Existence of Extreme Values)
Let f : S → R be a continuous real-valued function where S is a non-empty compact subset of R n . Then f has its maximum and minimum values. That is, there exists vectors x and x such that

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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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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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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 realizing!!

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Prisoners’ Dilemma: Analysis (**3**)
(Silent, Silent) looks mutually beneficial outcomes, though
Playing Confess is optimal regardless of other player’**s** choice!
Acting optimally ( Confess , Confess ) rends up realizing!!

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Both the Bertrand and Cournot models are particular cases of a more general model of oligopoly competition where firms choose prices and quantities (or capacities.). Ber[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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A tree starts with the initial node and ends at.. terminal nodes where payoffs are specified..[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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