1. Considered the following market . Chrome can choose when launching its new product either to do it LARGE or as NICHE . After Chrome has chosen its action , Firefox observes Chrome's choice and then can choose to ADAPT to RETAIN its own product . After Firefox has chosen its action , the game ends and the payoffs are made . The payoffs are as follows . If Chrome chooses LARGE and Firefox ADAPT the payoffs are 25 and 40 to Chrome and Firefox , respectively . If Chrome goes LARGE and Firefox RETAINS the payoffs are 30 and 50 to Chrome and Firefox . If Chrome plays NICHE and Firefox ADAPTS , the payoffs are (40 Chrome , 30 Firefox ) and if Chrome plays NICHE and Firefox RETAINS the payoffs are (20, 20 ) for Chrome and Firefox , respectively a. What is a Nach equilibrium ? Outline the Nach equilibrium or equilibria in the game , and explain your answer b. What is a subgame perfect equilibrium and how would you find such an equilibrium ? What is outcome in the the subgame perfect equilibrium in this game ? Explain your answer c. Does the subgame perfect equilibrium equilibrium result in the outcome that maximizes total surplus ? If it is, explain why . If not, is there any way the surplus maximizing outcome can be obtained ? Interpret your answer in the context of the Coage Theorem . Why might your solution not work ? 2. Two workers (workers ] and 2) on a production lime both have the choice to come to work Late or Early . If both come Late their payoffs are 5 and 4 to worker 1 and 2, respectively . If worker I comes Late and worker 2 comes Early the payoffs are 2 to each worker . If worker 1 comes Early and 2 comes Late the payoffs are I to each of them . Finally , if both workers come Early the payoffs are 3 to each worker Draw the normal form of this game and determine all of the Nach equilibria . Do you think this game could represent a true production process ? 3. Consider the following delegation versus centralization model of decision making loosely based on some of the discussion in class A principal wishes to implement a decision that has to be a number between 0 and 1; that is , a decision d needs to be implemented , where 0 g d g 1. The difficulty for the principal is that she does not know what decision is appropriate given the current state of the economy , but she would like to implement a decision that exactly equals what