An antique cabinet is being sold by means of an English auction.There are four bidders, Penelope, Marilyn, Irene, and Betsy.These bidders are unacquainted with each other and do not collude.Penelope values the cabinet at $1,600, Marilyn values it at $1,350, Irene values it at $2,100, and Betsy values it at $1,100.If the bidders bid in their rational self-interest, the cabinet will be sold to

A) Irene for about $2,100.
B) either Irene or Penelope for slightly more than $1,600.Which of them actually gets it is randomly determined.
C) Penelope for about $1,600.
D) Irene for slightly more than $1,600.
E) None of the above.

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MONIQUE BEATON · Accepted Answer

Final Answer : D, Explanation :  Irene values the cabinet the most and therefore would be willing to pay the highest price for it. However, if Irene bids $2,100, she would only win the cabinet if none of the other bidders value it at or above that price. Penelope's valuation is the closest to the $1,600 estimated value of the cabinet and therefore she may be willing to bid up to that amount. Betsy values the cabinet the least and is unlikely to bid very high for it. If Marilyn bids less than her valuation, she will have an incentive to bid the full $1,350 in order to win the auction. Therefore, it is rational for Irene to bid slightly more than $1,600 in order to outbid Penelope and possibly Marilyn, but not so high that she pays her entire valuation. Therefore, the cabinet is likely to be sold to Irene for slightly more than $1,600.

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