You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125
You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter17: Making Decisions With Uncertainty
Section: Chapter Questions
Problem 17.5IP
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1. Individual Problems 18-1
You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid.
The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur.
On the following table, indicate the price paid by the winning bidder.
Combination Number
|
Bidder 1 Value
|
Bidder 2 Value
|
Bidder 3 Value
|
Probability
|
Price
|
---|---|---|---|---|---|
($)
|
($)
|
($)
|
|||
1 | $88 | $88 | $88 | 0.125 | |
2 | $88 | $88 | $110 | 0.125 | |
3 | $88 | $110 | $88 | 0.125 | |
4 | $88 | $110 | $110 | 0.125 | |
5 | $110 | $88 | $88 | 0.125 | |
6 | $110 | $88 | $110 | 0.125 | |
7 | $110 | $110 | $88 | 0.125 | |
8 | $110 | $110 | $110 | 0.125 |
The expected price paid is
.
Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each other. The probabilities of the combinations of bidders are still all equal to 0.125. Continue to assume that the winning bidder must pay a price equal to the second highest bid.
On the following table, indicate the price paid by the winning bidder.
Combination Number
|
Maximum of Bidder 1 and 2
|
Bidder 3 Value
|
Probability
|
Price
|
---|---|---|---|---|
($)
|
($)
|
|||
1 | $88 | $88 | 0.125 | |
2 | $88 | $110 | 0.125 | |
3 | $110 | $88 | 0.125 | |
4 | $110 | $110 | 0.125 | |
5 | $110 | $88 | 0.125 | |
6 | $110 | $110 | 0.125 | |
7 | $110 | $88 | 0.125 | |
8 | $110 | $110 | 0.125 |
With collusion, the expected price paid is
.
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