Solve in detail

2. Two potential buyers compete for an indivisible item worth $12. Buyer 1 has $9 and buyer 2 has $6. The seller will not accept any offer less than $3. The buyers take turns bidding, starting with buyer 1. All bids are whole dollars and cannot exceed $12. A player can bid more than the amount of cash he holds, but if he wins he is punished severely, an outcome worse for him than any other. When one of the bidders does not raise the bid, the auction is over and the other player gets the item for the amount of his last bid. (a) Show that in all subgame perfect equilibria of the extensive game that models this situation player 1 gets the item. (b) Show that the game has a subgame perfect equilibrium in which the item is sold for $3. (c) Show that the game has a subgame perfect equilibrium in which the item is sold for $8