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The next theorem guarantees the existence of equilibrium ( 均衡の存在 ). Thm Consider a production economy (u i , e i , θ ij , Y j ) i∈I,j∈J . Suppose that the following conditions are satisfied: ◮ Utility function u i is continuous, strongly increasing, and strictly

Consider a consumer problem. Suppose that a choice function x(p; !) satis…es Walras’s law and WA. Then, show that x(p; !) is homogeneous of degree zero. 6. Lagrange’s Method You have two …nal exams upcoming, Mathematics (M) and Japanese (J), and have to decide how to allocate your time to study each subject. After eating, sleeping, exercising, and maintaining some human contact, you will have T hours each day in which to study for your exams. You have …gured out that your grade point average (G) from your two courses takes the form

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

This  is  an  advanced  course  in  microeconomics,  succeeding  to  Advanced  Microeconomics  I  (ECO600E)  in  which  we  study  individual  economic  decisions  and  their  aggregate [r]

(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).

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

5. Focal Point (5 points, bonus!) Choose one course offered in GRIPS in the winter term, and write down the name (do NOT write more than one names!). If the course you choose becomes the most popular answer, you would get 5 points. Otherwise, you would get 0 point. You need not explain the reason why you choose that course.

Similarly, player 2 must be indi¤erent amongst choosing X and Y , which implies 4q + 6(1 q) = 7(1 q) , 5q = 1 , q = 1=5. Thus, the mixed-strategy equilibirum is that player 1 takes A with probability 1=5 (and B with probability 4=5) and player 2 takes X with probability 3=4 (and Y with probability 1=4).

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…

(nw1) means student s prefers an empty slot at school c to her own assignment, and (nw2) and (nw3) mean that legal constraints are not violated when s is assigned the empty slot without changing other students’ assignments. The second property is about no-envy, which is also widely used in the context of school choice. But due to the structure of controlled school choice, as in Definition 1, even when a student prefers a school to her own and there is a student with lower priority in the school, the envy is not justified if the student’s move violates the legal constraints. Definition 2 formally states the condition for a student to have justified envy.

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.

You and your n − 1 roommates (n ≧ 2) each have five hours of free time that could be used to clean your apartment. You all dislike cleaning, but you all like having a clean apartment: each person i’s payoff is the total hours spent (by everyone) cleaning, minus a number c (> 0) times the hours spent individually cleaning. That is,

   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]

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]

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!!

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!!

   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]

Review of Lecture 5    Indifference property in mixed strategy NE.   If a player chooses more than one strategy with positive probability, she must be indifferent among such pure strategies: choosing any of them generate same expected payoff.

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

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]