博弈论作业代写 Game Theory Department of Economics

Ecn 122 -Game Theory Department of Economics

博弈论作业代写 If neither of you puts a check in the box then I neither add nor subtract any points."The professor grades "on the curve" as follows

HOMEWORK # 1 (for due date see web page)  博弈论作业代写

1.Ann,Bob and Carla have decided to bring some excitement into their lives with the help of their uncle Sam. Each
of them is going to secretly write a number chosen from the set (2,3,4} on a piece of paper and hand it to Sam Sam computes half the average of the three numbers, call it a, and determines the winners as those whosc number is closest to a. For example, suppose that Ann writes 2, Bob writes 2 and Carla writes 4. Then a =12+2+4= 1.33 and the winners are Ann and Bob. Sam then hands out money as follows: nothing to the2 loser(s. S2 to the winner if there are no ties and $1 to each of the winners if there are ties. Thus in the above example Ann and Bob get $1 and Carla gets nothing.

(a)Represent this game as a strategic-form game (let Ann choose the rows, Bob the columns and Carla the matrices). Assume that each player is selfish and greedy (i.e. only cares about how much money he/she gets and prefers more money to less).

(b)For every pair of strategies of Ann, x and y. Establish whether x dominates y (specify whether it is weak or strict dominance). y dominates x or neither.  博弈论作业代写

(c) Does Ann have a (weakly or strictly?) dominant strategy?(d) Is there a dominant-strategy equilibrium?

2.()There were only two students in a Game Theory class. They thought their professor was a nice guy but when they got their final exam (the only exam on which the class grade will be based) . They found on the first page a box with the following instructions:"You can check this box if you like. If you check your box and the other studen does not check hers.  Then I will give you an extra 10 points. Conversely, if you don't check your box and the othel student checks hers. then I will give her an extra 10 points.  If both of you check your respective boxes then I will take away 10 points from cach of you.

If neither of you puts a check in the box then I neither add nor subtract any points."The professor grades "on the curve" as follows: anybody with a final-exam score less than or equal to the mean gets a B and anybody with a final-exam score greater than the mean gets an A. The mean is calculated on the adjusted score. That is, the score after the extra 10 points are added or subtracted (depending on whether or not tho students check the boxes. as explained above).

The two students are Al and Brynn. Denote by a the score that Al got in the Midterm exam and b the score that Brynn got in the Midterm exam (the Midterm was just for practice and does not affect the class grade). Assume that both Al and Brynn came to the Final expecting that they each would get the same exam score as in the Midterm (that is, before they found out about the checking-the-bon business). Assume that each student only cares about . What grade he/she gets (e.g. getting an A when the other gets an A is as good as getting an A when the other gets a B).

(al) For each of the following cases represent the above situation as a game:  博弈论作业代写

(i)a=b(ii)a-b>10(ii)b-a>10(iv)0<a-b<10(v)0<b-a<10
(a2)For each of the five cases above, determine whether each student has a dominant strategy. Specify whether it is a weakly or strictly dominant strategy.

(b)The following year the same class has three students. The professor plays the same trick in the final: he puts a box with the following instructions. "You can check this box if you like. If you check your box and the other students do not, then I will give you an extra 10 points.

If two or more of you put a check then I will subtract 10 points from the score of all those. And only those, who put a check". The grading is as before anybody with a score greater than the mean gets an A and anybody with a score less than or equal to the mean gets a B. Assume that the three students are equally good and went to the final expecting to get the same score (again, this was before they found out about the box business). Each student only cares about his/her grade.The students are Alice.Bob and Carla.(b1) Represent this situation as a game.

(b2) Do the students have a (weakly/strictly) dominant strategy?  博弈论作业代写
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