$1)$ Nestl$\text{'}$s has over one hundred production facilities that all purchase hair nets and other hygienic supplies through independent suppliers. Nestl$$ created a centralized purchasing system that is cumbersome to use and has the potential to bargain for lower prices. Suppose that a division can purchase hairnets for $$8$ independently. If they all purchase through the central system, hairnets cost $$6.$ But if one division uses the system and the other purchases independently, the cost to the first is $$9$ while the cost to the second is $$7.$ What does the simultaneous move game look like and what is the equilibrium?