You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $28 or $35 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid.
The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur.
On the following table, indicate the price paid by the winning bidder.
Bidder 1 Value
Bidder 2 Value
Bidder 3 Value
Probability
Price
($)
($)
($)
The expected price paid is
.
Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each other. The probabilities of the combinations of bidders are still all equal to 0.125. Continue to assume that the winning bidder must pay a price equal to the second highest bid.
On the following table, indicate the price paid by the winning bidder.
Maximum of Bidder 1 and 2
Bidder 3 Value
Probability
Price
($)
($)
With collusion, the expected price paid is
.
You hold an oral- or English- auction among three bidders- You estimat.docx
1. You hold an oral, or English, auction among three bidders. You estimate that each bidder has a
value of either $28 or $35 for the item, and you attach probabilities to each value of 50%. The
winning bidder must pay a price equal to the second highest bid.
The following table lists the eight possible combinations for bidder values. Each combination is
equally likely to occur.
On the following table, indicate the price paid by the winning bidder.
Bidder 1 Value
Bidder 2 Value
Bidder 3 Value
Probability
Price
($)
($)
($)
The expected price paid is
.
Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their
values, but the two bidders would not be willing to bid against each other. The probabilities of
the combinations of bidders are still all equal to 0.125. Continue to assume that the winning
bidder must pay a price equal to the second highest bid.
On the following table, indicate the price paid by the winning bidder.
Maximum of Bidder 1 and 2
Bidder 3 Value
Probability
Price
($)
2. ($)
With collusion, the expected price paid is
Bidder 1 Value Bidder 2 Value Bidder 3 Value
Probability Price
($) ($) ($)
$28 $28 $28 0.125
$28 $28 $35 0.125
$28 $35 $28 0.125
$28 $35 $35 0.125
$35 $28 $28 0.125
$35 $28 $35 0.125
$35 $35 $28 0.125
$35 $35 $35 0.125
