William and Mike share an apartment Where each one of them has his own room. They want to decorate their apartment. Each one has two paintings and must decide how many to place in his own room and how many to place in the common living room. Suppose that the decision is made privately and that once the paintings are in their place, they cannot be removed. Let mm and 33m be the number of paintings that William and Mike, respectively, decide to place in their own room (thus, $l=4-.'Bw-.'Bm is the number of paintings in the living room). William's utility function is mow\"), an) =zrw(1.5+x;) and Mike's is um(:vm, an) =mm(1.5+:r:g). Then, for instance, if Mike places one painting in his own room and William two paintings in his room: mmzl, mw=2, and 321:1, they get utilities um(1,l) 22.5 and uw(2,l)=5, respectively. (a) Which are the strategies of each one of the roommates? (b) Represent the game in its normal form. (c) Find the unique Nash equilibrium of this game. Is this a good outcome for William and Mike