9781118041581

BIDDER STRATEGIES

A firm’s optimal bid in a given situation depends on many factors: its value for

the good at auction, its assessment of the extent of bidding competition, and

most important, the type of auction in which it competes.

To model bidding behavior, we begin by considering the so-called inde-

pendent private valuesetting.Here, each bidder assesses an individual value

(orreservation price) for the item up for bid. We denote buyer i’s value by vi, for

i 1... n, where n denotes the number of bidders. (In the converse case of a

competitive procurement, each firm would hold a private cost estimate ci.)

Each bidder’s value is independent of the others’ and is private: that is, it is

known only to itself. Although values are private, all bidders are aware of the

common probability distribution from which buyer values are independently

drawn. (After the fact, buyers hold different values. But before the fact, one

buyer is no more likely to have a high value than any other.) If winning bidder

i obtains the item at price P, its profit is simply viP. We now consider three

common types of auction.

English and Dutch Auctions

In the oral, ascending English auction, bids continually increase until the last

and highest bidder wins the item at his or her bid price. Optimal bidder strate-

gies in the English auction are remarkably simple:

When buyers hold independent private values, each buyer’s dominant strategy

in an English auction is to bid for the good up to the buyer’s reservation price

if necessary.

In the English auction, a buyer never should place a bid above his or her true

value; this would imply a loss if the bid were to win. Nor should the buyer stop

short of his or her value; this needlessly precludes earning a profit should a

slightly higher bid win. Bidding up to full value (if necessary) is optimal regard-

less of the competitors’ values or the bid strategies they might use; that is, this

strategy is dominant. Notice that the bidding stops when the price barely rises

above the next-to-last bidder’s value. Thus, the auction delivers the good to the

buyer holding the highest value among the bidders. The price in the English

auction stops at a level approximately equal to the second-highest reservation

price: PEv2nd.

The seller can achieve exactly the same price result using a closely related

auction method: the so-called Vickrey auctionor second-price auction. In the

Vickrey auction, bidders submit sealed bids, and the highest bidder claims the

item but pays a price equal to the second-highest bid(instead of paying his own

bid). It is easy to check (see Problem 1) thatin the second-price auction, each buyer’s

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