question on economics nash qurilibrium from subquestion a to e

A seller has a single good for sale. The seller decides on a price p to set for her good, and she can either set a high price p or a low price p, where p '.> E- The buyer observes the price Set by the seller and then decides whether or not to purchase the good. The buyer derives value 1!: > i from consuming the goodI and the seller derives no benet from retaining the good. (a) Formulate this interaction between the seller and the buyer as a game in strategic form. (b) Show that trade occurs in all Nash equilibria of this game. Put differently, there is no Nash equilibrium of this game in which the buyer does not end up with the seller's good. (c) Find a pure strategy Nash equilibrium of this game in which the buyer pays price i for the good. (d) Find a mixed strategyr Nash equilibrium of this game in which the buyer pays price 2 for the good. (e) Does this game have a mixed strategy Nash equilibrium in which the seller sets both prices a and E with positive probability