2) Assume there are two bidders who are competing at a private-value auction, decided by a sealed bid, first price mechanism. Let v, and b, denote your valuation and bid and let v and by denote the valuation and bid of the other bidder. If you outbid your opponent (b> b)), your payoff is (vi-bi), otherwise zero. While your opponent's valuation is private information and unknown, you know that it is uniformly distributed between 0 and 1, thus F(v)=P(v

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2) Assume there are two bidders who are competing at a private-value auction, decided
by a sealed bid, first price mechanism. Let v and b; denote your valuation and bid and let v
and bj denote the valuation and bid of the other bidder. If you outbid your opponent (bi> b), your
payoff is (v- bì), otherwise zero. While your opponent's valuation is private information and
unknown, you know that it is uniformly distributed between 0 and 1, thus F(v)= P(v < v) = v. You
also believe that the other bidder bids according to the function b(v) = v. Assuming your
valuation is v= 3/5, what is your optimal bid? How will your optimal bid change with additional
competitors in the auction? Justify your rationale.
Transcribed Image Text:2) Assume there are two bidders who are competing at a private-value auction, decided by a sealed bid, first price mechanism. Let v and b; denote your valuation and bid and let v and bj denote the valuation and bid of the other bidder. If you outbid your opponent (bi> b), your payoff is (v- bì), otherwise zero. While your opponent's valuation is private information and unknown, you know that it is uniformly distributed between 0 and 1, thus F(v)= P(v < v) = v. You also believe that the other bidder bids according to the function b(v) = v. Assuming your valuation is v= 3/5, what is your optimal bid? How will your optimal bid change with additional competitors in the auction? Justify your rationale.
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