4. [15 pts] There are N 2 2 collectors who engage in the auction of an antique. The collectors have a common valuation of the antique, denoted by c, which is known to all. The collectors make a simultaneous bid. Let pn denote the bid by collector n = 1,-- - ,N. The one with the highest bid wins the antique. The winner receives payoff v pi. The other(s) receive zero payoff. If more than one collectors make the same highest bid, then they have an equal chance of winning the item. Prove that: (a) It is not a Nash Equilibrium (NE) if the highest bid is v and only one collector bids this price. (b) It. is not a NE if the highest bid is less than c. (c) It is 8. NE that the highest bid is 1) and more than one collector bids this price