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Managerial and Decision Economics Auctions, Lecture notes of Managerial Economics

University of PortsmouthManagerial Economics

Different types of auctions such as English and Dutch auctions, sealed bid auctions, and models of bidders' valuations. It also discusses the winner's curse and optimal bidding strategies for different types of auctions. useful for students studying economics and business who want to understand the theory behind auctions and how to bid optimally in different auction settings.

Typology: Lecture notes

2021/2022

Available from 06/20/2022

Ludovicamazzocchi
Ludovicamazzocchi 🇬🇧

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Lecture 5
MANAGERIAL AND DECISION ECONOMICS
AUCTIONS
•The English auction a.k.a. the ascending bid auction begins by initially setting a low price which is then
successively raised until only one bidder remains.
-•Auction houses e.g. antiques
-•Cars, properties, dwellings
•The Dutch auction a.k.a the descending bid auction is opposite to above. Price is initially set very high
and lowered until it reaches a level at which a bidder is prepared to pay.
-•Aalsmeer Flower Auction
-•Agricultural products
•In the first price sealed bid auction, each bidder independently submits a single bid, without seeing the
bids submitted by other bidders. The highest bidder wins.
-•Premier League broadcasting rights
-•Rights to extract gas and minerals
•In the second price sealed bid auction a.k.a. the Vickrey auction, each bidder again independently
submits a sealed bid but the highest bidder pays the second highest bid.
-•Google AdWords
-•eBay
•MODELS OD BIDDERS’ VALUATIONS
Asymmetric information is a key element in auctions!
•Seller does not have perfect information about bidders’ valuations.
•Bidders do not have perfect information about each other’s valuations.
1. In the pure common value model, there is a single intrinsic value of the item that is the same for all
bidders. No single bidder, however, knows what this true value is and each bidder estimates the item’s
true value independently.
2. In the independent private value model, each bidder knows the true value of the item to him or herself
personally. Personal valuations of the item differ between bidders.
3. Affiliated valuations model includes elements of both models mentioned above and is a more realistic
model to represent the actual distribution of bidders’ preferences.
THE WINNER’S CURSE
Suppose an item is being auctioned where there is a single, intrinsic value of the item and this value is the
same for all bidders yet unknown precisely to any individual bidder.
Auction setting is:
•Sealed bid auction.
•Pure common value model.
Each bidder forms an unbiased private estimate of the true value of the item being auctioned.
Each bidder is equally likely to overvalue or undervalue the item, but if it were a large number auctions (i.e.
series of auctions) no bidder would systematically overvalue or undervalue the item.
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Lecture 5 MANAGERIAL AND DECISION ECONOMICS AUCTIONS

  • The English auction a.k.a. the ascending bid auction begins by initially setting a low price which is then successively raised until only one bidder remains.
    • (^) • Auction houses e.g. antiques
    • (^) • Cars, properties, dwellings
  • The Dutch auction a.k.a the descending bid auction is opposite to above. Price is initially set very high and lowered until it reaches a level at which a bidder is prepared to pay.
    • (^) • Aalsmeer Flower Auction
    • (^) • Agricultural products
  • In the first price sealed bid auction, each bidder independently submits a single bid, without seeing the bids submitted by other bidders. The highest bidder wins.
    • (^) • Premier League broadcasting rights
    • (^) • Rights to extract gas and minerals
  • In the second price sealed bid auction a.k.a. the Vickrey auction, each bidder again independently submits a sealed bid but the highest bidder pays the second highest bid.
    • (^) • Google AdWords
    • (^) • eBay
  • MODELS OD BIDDERS’ VALUATIONS Asymmetric information is a key element in auctions!
    • Seller does not have perfect information about bidders’ valuations.
    • Bidders do not have perfect information about each other’s valuations.
  1. In the pure common value model , there is a single intrinsic value of the item that is the same for all bidders. No single bidder, however, knows what this true value is and each bidder estimates the item’s true value independently.
  2. In the independent private value model , each bidder knows the true value of the item to him or herself personally. Personal valuations of the item differ between bidders.
  3. Affiliated valuations model includes elements of both models mentioned above and is a more realistic model to represent the actual distribution of bidders’ preferences. THE WINNER’S CURSE Suppose an item is being auctioned where there is a single, intrinsic value of the item and this value is the same for all bidders yet unknown precisely to any individual bidder. Auction setting is:
    • Sealed bid auction.
    • Pure common value model. Each bidder forms an unbiased private estimate of the true value of the item being auctioned. Each bidder is equally likely to overvalue or undervalue the item, but if it were a large number auctions (i.e. series of auctions) no bidder would systematically overvalue or undervalue the item.

Hence formally, estimated value of each bidder is

v+e_i

where v is the true, common value and e_i is the ‘error term’ associated with the bidder i ’s estimate. If each bidder bids their estimated value, the person with the highest value of e_i (e_max) wins the auction. However, if e_max>0 , the bidder pays more than the value of the good. They are likely to have over-estimated the value. This is the winner’s curse!

- How to overcome it? Theoretical research on auctions has shown that the expected value of true valuation given your signal is the highest signal is a decreasing function of auction size (number of participants). where d(N) is a discount factor for auction’s size. d(1)=1 and d(N) decreases as N increases. - The larger the value of N the greater is the likelihood that e_i being the highest signal v+e_i represents an overvaluation of v+e_i_._ HENCE: the optimal strategy in a common value model is to bid less than your estimated value. The more bidders there are, the lower your bid should be. OPTIMAL BIDDING STRATEGIES: I. English (ascending bid) auction A bidder’s optimal strategy is to continue to bid for as long as the price is below their private value, and to withdraw as soon as the price equals or exceeds this private value. - i.e. if another bidder is offering a price below that of your private value, you lose nothing by entering a revised bid. II. Second price (sealed bid) auction A bidder’s optimal strategy is to enter a bid equivalent to his or her own private value. In both an English auction and a second price auction, it pays to tell the truth. At the dominant strategy equilibrium, the outcomes of the English and second price sealed bid auction are the same. The bidder with the highest private value always wins, and always pays a price equal to the second-highest bidder’s private value.