4. Two roommates, Alfred and Bertie, share an apartment. Neither Alfred or Bertie enjoy putting in the effort to clean the flat, but both benefit from living in a clean place. On Sundays, both simultaneously decide how much time in their day they will devote to cleaning. If Alfred spends cA0 hours cleaning and Bertie spends cB0 hours cleaning, Alfred gets benefit cA+cB from the cleaner flat but pays opportunity cost cA for the time he spends on cleaning. Bertie is a bit of a clean freak, so he gets benefit ca+cB from the cleaner flat, where >1, but also pays opportunity cost of cB for the time he spends on cleaning. (a) Describe this situation as a game in strategic form. (b) If Bertie intends to spend cB0 hours cleaning, derive the best-response of Alfred. Do the same for Bertie, that is, if Alfred intends to spend cA0 hours cleaning, derive the best-response of Bertie. (c) Show that this game has a unique Nash equilibrium in which Bertie does all the cleaning