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Auction theory, Winner's Curse and revenue equivalence

Question (1): Explain what, in auction theory, is meant by the "winner's curse'?

Question (2): State the revenue equivalence theorm, explaining the terms involved.

Question (3): Why, in the case of private values, is an English auction similar to a second-price sealed bid auction?

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See the attached file for complete work. Some of the symbols may not print here correctly. Thanks

Question (1)
Explain what, in auction theory, is meant by the "winner's curse'?

In common value auctions with incomplete information, the value of item under auction is roughly same for all the bidders but the bidders do not know the item's market value when the bid. Since each bidder is estimating the value of the item independently and on an average they estimate the true value of the item correctly but as the winner is the highest bidder, the winner tends to overestimate the item's value overpay and regret it later. This phenomenon is known as winner's curse.

Example: Single item auction whose value to the bidders is not known with certainty in second-price sealed bid auction

Each bidder bid will be based on his estimate, based on information available to him/her. The item has a common value v, (which is same for all bidders but unknown to them). Suppose each bidder j =1,...,J has an estimate tj of v. These ...

Solution Summary

This post explains in simple words as well as mathematically three key theories of auction. The theories explained are winner's curse, revenue equivalence theorem and similarity of a second price sealed bid auction and English auction in case of private values (approx 800 words)

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