A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $100.There are two bidders.The dealer believes that there are only three possible values that each bidder's willingness to pay might take, $7,300, $2,600, and $100.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

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The dealer's expected revenue is the sum of the probabilities of each possible outcome multiplied by the corresponding revenue. The possible outcomes are that the highest bid is $7,300, $2,600, or $100. The probability of each outcome is 1/9, since there are 3 possible values for each bidder's willingness to pay and the probabilities are independent. The revenue from each outcome is $7,300, $2,600, or $0, respectively. Therefore, the dealer's expected revenue is (1/9) * $7,300 + (1/9) * $2,600 + (1/9) * $0 = $3,333.33.

A Dealer Decides to Sell an Antique Automobile by Means