You and a classmate are assigned a project on which you will receive one combine
ID: 1250853 • Letter: Y
Question
You and a classmate are assigned a project on which you will receive one combined grade. You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation:
-If both of you work hard, you both get an A, which gives each of you 40 units of happiness.
-If only one of you works hard, you both get a B, which gives each of you 30 units of happiness.
-If neither of you works hard, you both get a D, which gives each of you 10 units of happiness.
-Working hard costs 25 units of happiness.
a. Fill in the payoffs in the following decision box:
Your Decision
Work Shirk
Classmate's Decision Work (?,?) (?,?)
Classmate's Decision Shirk (?,?) (?,?)
b. What is the likely outcome?
c. If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)?
d. Another classmate cares more about good grades: He gets 50 units of happiness for a B, and 80 units of happiness from an A. If this classmate were your partner (but your preferences were unchanged), how would your answers to parts (a) and (b) change? Which of the two classmates would you prefer as a partner? Would he also want you as a partner?
Explanation / Answer
a) Your Decision Work Shirk Clasmates decision work (15,15) (30,5) Classmates Decision shirk (5, 30) (10,10) For this you look at each players decision whether to work or shirk and allocate the payoffs based on that decision. For example, if both decide to work they both receive a payoff of 40, however both did hard work which costs them 25 units so they both end up with 15 units in the end. b) The Nash equilibrium in this game is the joint decision to shirk. When evaluating a problem like this it is easiest to look at one joint decision, for example both players work, given your classmate makes this decision can you become better off by selecting a different option? In this case yes, you can. You would select to shirk due to the higher payoff. Then given you change how would the other player react? Well he would also choose to shirk given the higher payoff. Given your classmates change to shirk will you change your behaviour? No, you won't because the payoff is higher if you continue to shirk. Thus, you have arrived at your Nash Equilibrium. c) If you are partnered with the same person for a series of projects it is likely that over time you will put in place some sort of agreement such that each of you work hard to get the higher payoff of (15,15) rather than the predicted payoff from shirking of (10,10). d) Your Decions work shirk New classmates decision work (15,55) (30, 25) New classmates decision shirk (5, 50) (10, 10) The Nash equilibrium in this case is for you to shirk and for your new classmate to work for a payoff of (30, 25). In this case, you would want the new classmate as your partner due to the higher pay off that you would get, however the new classmate would likely want a partner with similar payoffs as them as the Nash equilibrium in this scenario would be for both players to work. Hope this helps. Cheers!
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