9781118041581

Summary 697

SUMMARY

Decision-Making Principles

1. By maximizing the number of competitors and letting price be
   determined by “what the market will bear,” competitive bidding
   institutions compare favorably with the alternatives of one-on-one
   negotiation and posted pricing.


2. In a sealed-bid auction, each buyer faces a basic trade-off: The lower its
   bid, the greater its profit if it is accepted but also the lower the chance
   the bid will win.


3. If bidders are risk neutral and have symmetrically distributed
   independent private values, the expected price (in equilibrium) is
   identical in the English and sealed-bid auctions.

Nuts and Bolts

1. In an English auction in which bidders have private values, each buyer’s
   dominant strategy is to bid up to its value if necessary.


2. a. In a sealed-bid auction, the manager should assess the probability
   distribution of the best competing bid, H(b) and determine the
   optimal bid by maximizing E() (v b)H(b). If G(b) is the bid
   distribution of a single competitor, then H(b) [G(b)]n ^1.
   b. An alternative approach is to determine an equilibrium bidding
   strategy—one that is profit maximizing against competitors that also
   are using profit-maximizing strategies. If bidders are risk neutral and
   values are drawn independently from a common distribution, the
   common equilibrium bidding strategy is biE(vƒvvi), where v
   denotes the largest of the other bidders’ personal values.


3. The winner’s curse occurs when the highest bidder—having won because
   of excessive optimism about the item’s value—finds it has paid more than
   the item is worth. When there is common-value uncertainty, bidders must
   discount their original estimates of value, that is, determine the item’s value
   conditional on winning the auction, in order to avoid the winner’s curse.

Questions and Problems

1. In a second-bid auction, buyers submit sealed bids, and the highest
   bidder obtains the item for sale but pays the seller an amount equal to
   the second highest bid.
   a. Suppose buyers hold different private values for the item. Show that
   each player’s dominant strategy is to bid his or her true value in this

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