Question

3. Suppose you and your class mate have to do a group assignment. Both of you can decide to work or shirk. If you both work, then both will get a good mark but both incur the cost of working. If one person works, you get a bad mark but the person who shirked will not have to put in the effort. If both shirk then the students fail. The following table represents the individuals’ utilities (as always the first number is the payoff of the row player): classmate work shirk you work 4, 4 1, 5 shirk 5, 1 0, 0

(a) Find all pure-strategy Nash equilibria with purely selfish preferences. [ There is also a mixed-strategy NE, which we will pay no attention to here.]

(b) Drawing on your experience as a student, have you observed outcomes such as those predicted? Have you seen other outcomes? Discuss!

(c) Suppose, both students like each other and have other-regarding preferences with u(x, y) = x + y/2, where x is the own outcome, while y is the outcome for the other student. What is the Nash prediction under these preferences? Discuss.

(d) Suppose, both students have competitive preferences and care only about how much better or worse off they are compared to the other student. In other words, u(x, y) = x − y for both students. What is the Nash prediction now! Discuss.

(e) Suppose both students are inequality averse and lose half a unit of utility for each unit difference in payoffs. In other words u(x, y) = x ( x y )/2. Find all pure-strategy Nash equilibria and discuss.

Answer 1

IF YOU HAVE ANY DOUBTS COMMENT BELOW I WILL BE TTHERE TO HELP YOU..ALL THE BEST..

AS FOR HOMEWORKLIB RULES WE ANSWER ONE QUESTION ONLY..

I HOPE YOU UNDERSTAND..

PLS RATE THUMBS UP..ITS HELPS ME ALOT..

THANK YOU...!!