At dinner, mom made young Charlie and David their favorite pasta. Mom cooked about 2.5 plates/servings, and each young boy can eat much more than 2 plates. Here are some assumptions: first, they equally enjoy pasta and value it at 1 "enjoyment" per plate; second, they eat equally fast; third, if they both go up to get the pasta and there are not enough, they share what is remaining. Fourth, pasta tastes good while hot, so 80% discount if its not hot. Then what would their strategy be? To simplify our problem, let us restrain their strategy space to be getting full plate first or getting half plate first. Here is the normal form matrix: F H F 1.2, 1.2 1, 1.3 H 1.3, 1 1.1, 1.1 Q3.1: What would they do? (find the pure strategy NE) Q3.2: If this situation happens every night, what can mom do to make it better for them? (Specify a strategy if this game repeats infinitely). If Charlie goes up first to get pasta, how would that change the game? F David F H Charlie H David F H {A1, A2} {B1, B2} {C1,C2} {D1, D2} Q3.3: Are the payoffs ("enjoyments") different? Please find the numbers for {A1, A2}, {B1, B2} {C1,C2}, {D1, D2}. Q3.4: What are they going to do? (find the equilibrium path).