# トップPDF Comments on the Midterm Exam 最近の更新履歴 yyasuda's website

### Comments on the Midterm Exam 最近の更新履歴 yyasuda's website

 Standard deviation: 12.44 Comments:  The average performance is very good. I think most of you fully understand the basic concepts in the lecture. Those of you receive 40 or lower might better study much harder. The last handout “game theory chapter (from Nicholson and Snyder)” should be helpful to complement the materials in the lecture.

### PS3 最近の更新履歴 yyasuda's website

(b) Now suppose there are n(> 2) individuals. Then, can we find a competitive equilibrium? (How) Does your answer depend on n? 4. Question 4 (8 points) Consider a production economy with two individuals, Ann (A) and Bob (B), and two goods, leisure x 1 and a consumption good x 2 . Ann and Bob have equal en-

### Final1 最近の更新履歴 yyasuda's website

where α > 0 and 0 < β < 1. Let w 1 , w 2 > 0 be the prices for inputs x 1 and x 2 respectively. Then, answer the following questions. (a) Sketch the isoquant for this technology. Hint: Isoquant is the combination of inputs that achieves a given level of output y. (similar to “indifference curve” in consumer theory.)

### Final14 最近の更新履歴 yyasuda's website

C) Now suppose that the rule of the game is modified as follows. If exchange occurs,  each  individual  receives  3  times  as  much  amount  as  the  bill  she  will  have.  For  example, if individual 1 receives \$5 and 2 receives \$10 initially and both wish to  exchange,  then  1  will  receive  \$30  (=  \$10  x  3)  and  2  will  receive  \$15  (=  \$5  x  3).  Nothing  happens  if  they  do  not  exchange.  Then,  does  trade  occur  in  a  Bayesian  Nash equilibrium? Explain.

### Midterm2 最近の更新履歴 yyasuda's website

(a) Show that there is no pure-strategy equilibrium in this game. (b) Is there any strictly dominated strategy? If yes, describe which strategy is dominated by which strategy. If no, briefly explain the reason. (c) Derive the mixed-strategy Nash equilibrium.

### Lec10 最近の更新履歴 yyasuda's website

since there is no future play . The only possible outcome is a price war irrespective of the past history of the play.    In the second to the last period ( t = T-1 ), no firm has an incentive to collude since the future play will be a price war no matter how each firm plays in period T-1 .

20 さらに読み込む

### Lec2 最近の更新履歴 yyasuda's website

General Formulation of PD     The larger the payoff, the better the corresponding result.    Desirability of outcomes for each player:    g > c > d > l, that is, ( D , C ) > ( C , C ) > ( D , D ) > ( C , D )

27 さらに読み込む

### Lec1 最近の更新履歴 yyasuda's website

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!!

27 さらに読み込む

### Lec3 最近の更新履歴 yyasuda's website

   Choose a subway station in Tokyo and write down its name.    You will win if you can choose the most popular answer.    Most of the students are expected to write “xxx”.    Like this experiment, there may exist a Nash equilibrium which stands out from the other equilibria by some

20 さらに読み込む

### Midterm13 最近の更新履歴 yyasuda's website

2. Simple 2-2 Games (18 points, take your time) For the 2-2 games X, Y, and Z below, answer the following questions: i. Explain whether there exists a dominant strategy. ii. Find (all) pure-strategy Nash equilibrium if it exists. iii. Find (all) mixed-strategy Nash equilibrium if it exists.

### Final11 最近の更新履歴 yyasuda's website

B) Consider the two-period repeated game in which the above stage game will be played twice. Suppose that the payoff for each player is simply the sum of the payoffs in the stage games. Then, can (U, L) be sustained as a subgame perfect Nash equilibrium? If yes, derive the equilibrium. If not, explain why.

### Midterm12 最近の更新履歴 yyasuda's website

a) Find all pure strategy Nash equilibria. b) Find the mixed strategy Nash equilibrium in which each player randomizes over just the first two actions, i.e., A, B for P1 and D, E for P2, respectively. c) Is there a mixed strategy Nash equilibrium in which both players randomize over all three strategies? If yes, derive the equilibrium. If not, explain why.

### Slide1 最近の更新履歴 yyasuda's website

Combination of dominant strategies is Nash equilibrium. There are many games where no dominant strategy exists[r]

20 さらに読み込む

### Final13 最近の更新履歴 yyasuda's website

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 (\$).
さらに見せる

### Lec6 最近の更新履歴 yyasuda's website

Strategy and Outcome     Strategy in dynamic game = Complete plan of actions    What each player will do in every possible chance of move.    Even if some actions will not be taken in the actual play, players specify all contingent action plan.

16 さらに読み込む

### EX1 最近の更新履歴 yyasuda's website

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

### EX2 最近の更新履歴 yyasuda's website

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

### EX3 最近の更新履歴 yyasuda's website

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

### PS1 最近の更新履歴 yyasuda's website

(a) The intersection of any pair of open sets is an open set. (b) The union of any (possibly infinite) collection of open sets is open. (c) The intersection of any (possibly infinite) collection of closed sets is closed. (You can use (b) and De Morgan’s Law without proofs.)

### PS2 最近の更新履歴 yyasuda's website

Problem Set 2: Posted on November 4 Advanced Microeconomics I (Fall, 1st, 2014) 1. Question 1 (7 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.