Two students, 1 and 2, took a course with a professor who decided to allocate grades...

 

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Two students, 1 and 2, took a course with a professor who decided to allocate grades as follows: Two envelopes will each include a grade g, € {A, B, C, D, F}, where each of the five options is chosen with equal probability and the draws for each student i € {1,2} are independent. The payoffs of each grade are 4, 3, 2, 1, and 0, respectively. Assume that the game is played as follows: Each student receives his envelope, opens it, and observes her grade. Then each student simultaneously decides if she wants to hold on to her grade (call this option H) or exchange it with the other student (call this option X). Exchange happens if and only if both choose to exchange. If an exchange does not happen then each student gets her assigned grade. If an exchange does happen then the grades are bumped up by one. That is, if student 1 had an initial grade of C and student 2 had an initial grade of D, then after the exchange student 1 will get a C (which was student 2's D) and student 2 will get a B (which was student 1's C). A grade of A is bumped up to an A+, which is worth 5. (a) Assume that student 2 plays the following strategy: "I offer to exchange for every grade I get." What is the best response of student 1? Hint: the best response has to be type-dependent: that is, H or X is chosen depending on g₁. (b) Assume that student 2 plays the following strategy: "I offer to exchange only if my grade is C, D, or F." What is the best response of student 1? Two students, 1 and 2, took a course with a professor who decided to allocate grades as follows: Two envelopes will each include a grade g, € {A, B, C, D, F}, where each of the five options is chosen with equal probability and the draws for each student i € {1,2} are independent. The payoffs of each grade are 4, 3, 2, 1, and 0, respectively. Assume that the game is played as follows: Each student receives his envelope, opens it, and observes her grade. Then each student simultaneously decides if she wants to hold on to her grade (call this option H) or exchange it with the other student (call this option X). Exchange happens if and only if both choose to exchange. If an exchange does not happen then each student gets her assigned grade. If an exchange does happen then the grades are bumped up by one. That is, if student 1 had an initial grade of C and student 2 had an initial grade of D, then after the exchange student 1 will get a C (which was student 2's D) and student 2 will get a B (which was student 1's C). A grade of A is bumped up to an A+, which is worth 5. (a) Assume that student 2 plays the following strategy: "I offer to exchange for every grade I get." What is the best response of student 1? Hint: the best response has to be type-dependent: that is, H or X is chosen depending on g₁. (b) Assume that student 2 plays the following strategy: "I offer to exchange only if my grade is C, D, or F." What is the best response of student 1?

Answer rating: 100% (QA)

a In this situation understudy 2 generally offers to trade no matter what the grade got To decide the best reaction of understudy 1 we want to think a... View the full answer