Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.
Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.11P
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Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how
What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.
![The Federal Communications Commission (FCC) organizes multiple auctions of airwave
licenses each year that generate billions of dollars in revenue. The following is a simplified
version of an FCC auction. Consider three bidders bidding for two objects (for example, an
object could be a license that covers Manhattan, and a bidder can be Comcast). Let vij
be bidder i's valuation for object j, where i E {1,2,3} and j e {1,2}. Bidder i knows its
valuation
Vij
but other bidders only know that vij is drawn uniformly from [0, 100]. If bidder
i wins object 1 at price p1 and object 2 at price p2, bidder i's payoff is v;1 – Pi + Vi2 – P2.
If bidder i wins only object j at price p;, his payoff is vij – pj. If bidder i does not win any
object, his payoff is 0.
The auction proceeds as follows. The initial prices are zero for both objects. All bidders sit
in front of their computers and observe the prices for both items in real time. Initially all
bidders are invited to enter the bidding race for both items. At any moment in time, each
bidder has the option to withdraw from the bidding race for either object or both. If a bidder
withdraws from the bidding for one object, he can no longer get back to the bidding for that
object, but he can stay in the bidding race for the other object if he hasn't withdrawn from
it previously. The price for an object increase continuously over time as long as there are
'FYI. Early this year, FCC organized its 107th auction, where 57 bidders compete for 5,684 airwave
licenses for 5G networks. The total revenue from auction 107 is over 80 billion dollars. FCC's auction
designs have been adopted by many other countries in the world, and the auctions rules have been updated
from time to time. Microeconomic theorists are involved in both auction designs and actual bidding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa550ff16-be18-4c5b-b3ad-8a1f02d33310%2Fce1be06c-d383-4923-8ab0-d983ac95c9a0%2Fklaoaz_processed.png&w=3840&q=75)
Transcribed Image Text:The Federal Communications Commission (FCC) organizes multiple auctions of airwave
licenses each year that generate billions of dollars in revenue. The following is a simplified
version of an FCC auction. Consider three bidders bidding for two objects (for example, an
object could be a license that covers Manhattan, and a bidder can be Comcast). Let vij
be bidder i's valuation for object j, where i E {1,2,3} and j e {1,2}. Bidder i knows its
valuation
Vij
but other bidders only know that vij is drawn uniformly from [0, 100]. If bidder
i wins object 1 at price p1 and object 2 at price p2, bidder i's payoff is v;1 – Pi + Vi2 – P2.
If bidder i wins only object j at price p;, his payoff is vij – pj. If bidder i does not win any
object, his payoff is 0.
The auction proceeds as follows. The initial prices are zero for both objects. All bidders sit
in front of their computers and observe the prices for both items in real time. Initially all
bidders are invited to enter the bidding race for both items. At any moment in time, each
bidder has the option to withdraw from the bidding race for either object or both. If a bidder
withdraws from the bidding for one object, he can no longer get back to the bidding for that
object, but he can stay in the bidding race for the other object if he hasn't withdrawn from
it previously. The price for an object increase continuously over time as long as there are
'FYI. Early this year, FCC organized its 107th auction, where 57 bidders compete for 5,684 airwave
licenses for 5G networks. The total revenue from auction 107 is over 80 billion dollars. FCC's auction
designs have been adopted by many other countries in the world, and the auctions rules have been updated
from time to time. Microeconomic theorists are involved in both auction designs and actual bidding.
Transcribed Image Text:two or three bidders in the race for that object. The rate of price increase is 1; that is to
say, the price increases to x if x units of time has passed, where x is a real number. The
price for an object stops increasing if there is at most one bidder left for the bidding race for
the object, and the price will stay at that level for the rest of the game; we say the price is
locked in this case. (the price for the other object will continue to increase if more than one
bidder stays in the bidding race for that object). The auction ends as soon as both prices
stop increasing (i.e., at most one bidder remains in the bidding race for each object). An
object is sold to the bidder (if any) who remains in the bidding race for that object at the
locked price.
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