A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $600.There are two bidders.The dealer believes that there are only three possible values that each bidder's willingness to pay might take, $6,400, $3,000, and $600.Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the automobile is

Question

Quizplus · Accepted Answer

The expected revenue from an auction with two bidders can be calculated as follows:
- If bidder 1's value is greater than bidder 2's value, then the price will be set at the second-highest value (the value of the other bidder). The probability of this happening is 2/3.
- If bidder 2's value is greater than bidder 1's value, then the price will be set at the second-highest value. The probability of this happening is also 2/3.
- If both bidders have the same value, then the price will be set at that value. The probability of this happening is 1/3.

Given the possible values, the expected revenue for the dealer can be calculated as:

(2/3)*(6400+600)/2 + (2/3)*(3000+600)/2 + (1/3)*600 = $3,333.33

A Dealer Decides to Sell an Antique Automobile by Means