Economic- Game theory

Consider two pizza stores, Donna's Deep Dish and Pierce's Pizza Pies. These two pizza stores are competing with each other by price. The demand functions for their pizza are: QPierce = 12 _ PPiarca + 0-51) Donna Qonno = 12 _ Ponno + 0-51: Pierce The marginal cost to make each pizza for these two pizza stores is $3. a. What prices do the rms choose in equilibrium\"? How much prot does each rm earn? opt) b. If the rms work together to maximize their joint prot, what prices do the rms choose in equilibrium? How much prot does each rm earn\"? (5th c. Suppose the two stores are in a repeated relationship, trying to sustain the joint prot- maximizing prices calculated 111 part (b). 'I'hey print new menus each month and thereby commit themselves to prices for the whole month. In any one month, one of them can defect from the agreement. If one of them holds the price at the agreed-upon level, what is the best defecting price for the other? What are its resulting prots? (Spt) d. For what interest rate will their collusion be sustainable if both are using the grim strategy? (Spt)