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You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $24 or $30 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.

You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $24 or $30 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.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please what is the expected price paid? 

and with collusion, the expected price paid?

You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $24 or $30 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Bidder 1 Value Bidder 2 Value Bidder 3 Value ($) ($) ($) Probability Price $24 $24 $24 0.125 $24 $24 $24 $30 0.125 $24 $24 $30 $24 0.125 $24 $24 $30 $30 0.125 $30 $30 $24 $24 0.125 $24 $30 $24 $30 0.125 $30 $30 $30 $24 0.125 $30 $30 $30 $30 0.125 $30 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.
Transcribed Image Text:You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $24 or $30 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Bidder 1 Value Bidder 2 Value Bidder 3 Value ($) ($) ($) Probability Price $24 $24 $24 0.125 $24 $24 $24 $30 0.125 $24 $24 $30 $24 0.125 $24 $24 $30 $30 0.125 $30 $30 $24 $24 0.125 $24 $30 $24 $30 0.125 $30 $30 $30 $24 0.125 $30 $30 $30 $30 0.125 $30 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.
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 $24 $24 0.125 $24 $24 $30 0.125 $24 $30 $24 0.125 $24 $30 $30 0.125 $30 $30 $24 0.125 $24 $30 $30 0.125 $30 $30 $24 0.125 $24 $30 $30 0.125 $30 With collusion, the expected price paid is $
Transcribed Image Text: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 $24 $24 0.125 $24 $24 $30 0.125 $24 $30 $24 0.125 $24 $30 $30 0.125 $30 $30 $24 0.125 $24 $30 $30 0.125 $30 $30 $24 0.125 $24 $30 $30 0.125 $30 With collusion, the expected price paid is $
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