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B) Nash equilibrium outcomes are always Pareto efficient. C) A strategy used in Nash equilibrium can never be eliminated in the process of iterated elimination of dominated strategies. D) In a mixed-strategy Nash equilibrium, each player must completely randomize his/her (pure-) strategies, i.e., taking every strategy with exactly equal probability. E) The Zermelo’s theorem says that the second mover always has a winning strategy.

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

2 units of the firm 1’s good and A − p 2 + p 1 2 units of the firm 2’s good. Assume that the firms have identical (and constant) marginal costs c(< A), and the payoff for each firm is equal to the firm’s profit, denoted by π 1 and π 2 .

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

(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.

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]

   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]

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

  4. Incomplete Information (16 points, think carefully)  There are four different bills, $1, $5, $10, and $20. Two individuals randomly receive  one bill each. The (ex ante) probability of an individual receiving each bill is therefore  1/4.  An individual knows only her own bill, and  is  simultaneously given the option of  exchanging her bill for the other individual’s bill. The bills will be exchanged if and only  if  both  individuals  wish  to  do  so;  otherwise  no  exchange  occurs.  That  is,  each  individuals can choose either exchange (E) or not (N), and exchange occurs only when  both  choose  E.  We  assume  that  individuals’  objective  is  to  maximize  their  expected  monetary payoff ($). 

   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]

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

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]

   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]

(a) If an agent is risk averse, her risk premium is ALWAYS positive. (b) When every player has a (strictly) dominant strategy, the strategy profile that consists of each player’s dominant strategy MUST be a Nash equilibrium. (c) If there are two Nash equilibria in pure-strategy, they can ALWAYS be Pareto

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