Question:Represent this game in a game tree. Solve for the Nash Equilibria of the game by backward induction. These are the subgame perfect Equilibria of the game, i.e. Equilibria in which players' actions are optimal in every subgame. Notice (N,W) is not a subgame perfect equilibrium because backward induction ensures that actions taken in equilibrium are optimal in every subgame, even those aren't reached in equilibrium.

1. The Market Entry Game Incumbent Pizza has been the sole pizza joint in Mytown, USA since 1974, and does a brisk business. When the old lady running the yarn shop across the street finally decides to retire to Florida, John D. Entrant, a local entrepreneur with a soft-spot for thin crusts, senses an opportunity. "There's plenty of room for two pizza joints in this town," he thinks, and starts making some calls. Mr. Incumbent hears of Mr. Entrants's plans, and calls Mr. Entrant. "Don't open a new shop," he threatens. "If you do, I'll price so low, you'll go out of business in no time." Naturally, we ask, is Mr. Incumbent's threat subgame perfect? We model this as an extensive form game. First, Mr. Entrant decides whether to enter (E) or not (N). Then, Mr. Incumbent decides whether to engage in a price war (W) or continue business as usual (U). If Mr. Entrant chooses N, he gets 0 and Mr. Incumbent continues to do a brisk business, making 100. If Mr. Entrant chooses E and Mr. Incumbent chooses W, Mr. Entrant gets -50 and Mr. Incumbent gets 0. If Mr. Entrant chooses E and Mr. Incumbent chooses U, then they each get 30