may be well below his reported bid. In short, he should report his true
value so that the auction house can bid on his behalf (exactly as he
would himself if he were present at the auction).- a. Against a single rival, the optimal bid is $2.4 million implying an
expected profit of (2.9 2.4)(.4) $.2 million. Against two rivals,
the optimal bid is $2.6 million implying an expected profit of
(2.9 2.6)(.6)^2 $.108 million.
b. Each firm’s equilibrium bidding strategy is
.
Thus, the optimal bid is (1/3)(2) (2/3)(2.9) $2.6 million.- a. A firm can only lose money by bidding above its value. Bidding below
one’s value risks getting neither position and can only help if moving
down to position two is more profitable than winning the top
position. Firm 1’s profit from winning the top position is: (50–35)(5)
75¢ per minute. If it were to bid just below 35¢, it would win the
second position at a price of 30¢, implying a profit of: (50–30)(3)
60¢ per minute. Neither firm 1 nor any other firm has a reason to bid
below value. Therefore, bidding one’s true value is an equilibrium.
b. Now if firm 1 bids just below 35¢ and wins the second position at 20¢,
its profit is: (50–20)(3) 90¢ per minute (greater than its profit from
bidding truthfully and winning the top position). Truthful bidding is
no longer optimal. - a. Under blind bidding, each firm’s reservation price is simply the
expected value of the film. The common expected value for each
bidder is (1/3)(10,000) (1/3)(6,000) (1/3)(2,000) $6,000,
and this will be the equilibrium bid for each in a sealed-bid auction.
Thus, the distributor’s revenue from the auction will exactly equal the
expected value of the film. If the distributor delays the bidding until
the uncertainty is resolved, exhibitors will bid the full (certain) value
of the film. Again the expected revenue is $6,000. However, if
exhibitors are risk averse, their reservation values (and, therefore,
bids) will be below the film’s expected value under blind bidding.
Bids for previewed films will be unaffected (since these films carry no
risk). With risk-averse bidders the exhibitor increases its expected
revenue by previewing the films.
b. Selective screening works only if bidders are naive. Sophisticated
bidders will anticipate that unscreened films are likely to have lower
expected box-office receipts than the rest of the films. They will bid
accordingly.
c. Against an astute bidder, the less well-informed theaters must bid
cautiously to avoid the winner’s curse, that is, winning films that the
astute bidder knows are poor box-office bets. This kind of bid
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