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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]

◮ Firm 1’s strategy is a quantity choice, but firm 2’s strategy is to specify her quantity choice in each possible marginal cost. Let q 2 H (= q 2 (c H 2 )) and q 2 L (= q 2 (c L 2 )) be the quantity selected by player 2 for each realization of the cost. Then, the optimization problem for each player is described as follows:

When we analyze the demand for a single good (partial equilibrium study), it would be convenient to aggregate “all other goods”. A Consumer’s Problem (again)[r]

   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]

   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]

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

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

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

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…

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

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!!

where J (/ M ) is the number of hours per day spent studying for Japanese (/ Math- ematics). You only care about your GPA. Then, answer the following questions. (a) What is your optimal allocation of study time? (b) Suppose T = 10. If you follow this optimal strategy, what will be your GPA?

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,

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!!

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]

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

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

    5. Bayesian Nash Equilibrium (12 points)  There are three different bills, $5, $10, and $20. Two individuals randomly receive one  bill each. The (ex ante) probability of an individual receiving each bill is therefore 1/3.  Each  individual  knows  only  her  own  bill,  and  is  simultaneously  given  the  option  of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff ($).