Consider an antique auction where bidders have independent private values. There
ID: 1097460 • Letter: C
Question
Consider an antique auction where bidders have independent private values. There are two bidders, each of whom perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?
A
Submit a bid of $150.
B
Submit a bid of $200.
C
Submit a bid that is less than $150.
D
Yell "mine" when the bid reaches $150.
A
Submit a bid of $150.
B
Submit a bid of $200.
C
Submit a bid that is less than $150.
D
Yell "mine" when the bid reaches $150.
Explanation / Answer
Answer: Yell "mine" when the bid reaches $150.
Let v be the valuation of the product as per the bidder (Sue) = $200
Let x be the bid placed by bidder (Sue) = ?
Now when x < v, it reduces chances of winning but at the same time it increases the profit as the bidder will now have to pay less than what his valuation is.
So there is a tradeoff between bid amount and valution and this will lead to bidding amount being less than the total valuation.
Therefore, in this case the bid will be less than $200.
Further, this is a dutch auction and the price will continue to drop further till a bidder places a bid and announces his / her acceptance to win. The first bid is actually the last bid in a dutch auction.
Therefore, the optimal strategy for Sue will be to "yell mine" when the price is dropped to $150 and she can earn a profit of $50.