Exercise 7 (Roommates voting) Three roommates; Sheldon. Leonard; and Howard. need to vote on whether they will adopt a new rule and clean their apartment once a week: or stick to the current once amonth rule. Each votes "yes\" for the new rule or "no " for the current rule. Sheldon and Leonard prefer the new rule while Howard prefers the old rule. (a). Imagine that the players require a unanimous vote to adopt the new rule. Sheldon votes rst. then Leonard}. and then Howard. the latter two observing the previous votes. Draw a game tree to describe this game and nd the Nash equilibria. (t). Imagine now that the three roommates require a majority vote to adopt the new rule (at least two \"yes " votes for the adoption of the new rule). Again). Sheldon votes rst. then Leonard. and then Howard. the latter two observing the previous votes. Draw a game tree to describe this game and nd the Nash equilibria. (c). Now imagine that the game is the same as in part (l3) except that the roommates put their votes into a hat so that the votes of earlier voters are not observed by the later voters and the votes are counted after all have voted. Will the Nash equil-ilrria be different from those in part (l3)