An antique cabinet is being sold by means of an English auction. There are four
ID: 1101141 • Letter: A
Question
An antique cabinet is being sold by means of an English auction. There are four bidders, Hester, Arabella, Gloria, and Desiree. These bidders are unacquainted with each other and do not collude. Hester values the cabinet at $1,200, Arabella values it at 500, Linda values it at $1,400, and Eva values it at $700. If the bidders bid in their rational self-interest, the cabinet will be sold to
(a) Gloria for about $1,400.
(b) Hester for about $1,200.
(c) either Gloria or Hester for about $1,200. Which of these two buyers gets it is randomly determined.
(d) Gloria for slightly more than $1,200.
(e) either Gloria or Hester for about 500. Which of these two buyers gets it is randomly determined.
(Please show work or explain. i already have the answer. just need to know how to solve it)
Explanation / Answer
I think the names are misplaced here. Linda should be Gloria and Eva should be Desiree.
(d) Gloria for slightly more than $1,200.
In the English auction, bidders can see bidding by other people. The maximum a person will bid is his or her value of the object.
Hence, max Hester will bid = $1200, max Arabella will bid = $500, max Gloria will bid = $1400 and max Desiree will bid = $700
Arabella's and Desiree's maximum bid will be met by Hester because he values the object more that them. In turn, Hester's maximum bid would be met by Gloria who values the object more than Hester. However, if Gloria bids just more than Hester's maximum bid of $1200, she would get the object. She has no gains from bidding her maximum valuation of $1400.