Question

Julie, Mike, Lilly need deciding to work- or-shirk for their assignment.

Payoffs are given as below:

1. Each member is going to receive the same grade.
2. If at least two members work the grade assigned will be good, giving each student four units of payoff.
3. If only one group member works the grade assigned will be mediocre, giving each student two units of payoff.
4. If no group member works the grade assigned will be bad, giving each student zero units of payoff.
5. Working implies an effort worth losing one unit of payoff.

Question (a): Create the payoff matrix for this three-player game.

Question (b): Does any player have a dominant strategy?

Question (c): What are the pure strategy Nash Equilibrium of the game?

Answer 1

a> Since it is a 3 player game, I will draw 2 payoff matrix of size 2x2. The payoff are in the order of Julie, Mike and Lily -

			Case 1 - Lily Works
			Mike
		works		shirks
	works	(3,3,3)		(3,4,3)
Julie
	shirks	(4,3,3)		(2,2,1)

			Case 2 - Lily Shirks
			Mike
		works		shirks
	works	(3,3,4)		(1,2,2)
Julie
	shirks	(2,1,2)		(0,0,0)

b> No player has a dominant strategy since if everyone else works, it is best to shirk and if everyone else shirks, it is best to work. Thus, dominant strategy does not exist.

c> The pure Nash strategy equilibrium would be where two people work and one shirk, i.e (W,W,S) OR (W,S,W) OR (S,W,W). Since if no one works, one can improve his payoff by 1 by working. If one works, then the same is true but not if two of them works. So, they are NE.