Consider a two-stage selling game in which a seller can sell one item to a buyer. In the first stage the seller makes a take-it or leave-it offer by announcing a price at which the seller is willing to sell the item. In the second stage the buyer decides whether to accept the offer or not. If the offer is accepted the item changes hands; otherwise no trade occurs. The buyer values the item at v and the seller values the item at c, with 1>v>c>0. The values c and v are publicly known.

(a) Can it be a Nash equilibrium that no trade takes place? If so, characterize a no- trade Nash equilibrium.

(b) Characterize the set of subgame perfect Nash equilibria.