1. Recall the two roommate game in which Albert and Victoria were each deciding whether or not to clean. The payoff matrix for this game is described below:

Victoria Clean Don't Clean Clean [5 5) [2 6) Alb It ' ' '3 Dona mean (3,3) (a) Suppose that we add a second stage to this game in which Victoria and Albert each have a chance to punish the other. Imagine that at the end of the day, Victoria and Albert are each able to see whether the other had done any housecleaning. After seeing what the other has done, each has the option of starting a quarrel. A quarrel hurts both of them, regardless of who started it. Thus, we will assume that if eitherl or both of them starts a quarrel, the day's payoff for each of them is reduced by 2. For example, if Victoria cleans and Albert doesn't, and if Victoria (upon seeing this result) starts a quarrel, Albert's payoff will be 6-2 =4 and Victoria's will be 2-2=0.) Assuming that each is trying to maximize his/her payoff, given the actions of the other, what would you expect each of them to do in the first stage of the game: clean or not clean? {bl Suppose instead that Victoria and Albert are governed by emotions that they cannot control. Neither can avoid getting angry if the other does not clean. And if either gets angry, they will quarrel so that the payoff of each is again diminished by 2. Given that there is certain to be a quarrel if either does not clean, the payoff matrix between Victoria and Albert becomes: Victoria Clean Don't Clean Albert Clean (55) Don't Clean I} Does this game have a dominant strategy equilibrium? How about a Nash equilibrium