# A seller intends to run a second-price, sealed-bid auction for an object. There are two bidders,…

A seller intends to run a second-price, sealed-bid auction for an object. There are two bidders, a and b, who have independent, private values vi that are either 0 or 1. For both bidders the probabilities of vi = 0 and vi = 1 are each 1 2 . Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. Half of the time his value is 1 and he is aware that it is 1; the other half of the time his value is 0 but occasionally he mistakenly believes that his value is 1. Let’s suppose that when b’s value is 0 he acts as if it is 1 with probability 1 2 and as if it is 0 with probability 1 2 . So in effect bidder b sees value 0 with probability 1 4 and value 1 with probability 3 4 . Bidder a never makes mistakes about his value for the object, but he is aware of the mistakes that bidder b makes. Both bidders bid optimally given their perceptions of the value of the object. Assume that if there is a tie at a bid of x for the highest bid the winner is selected at random from among the highest bidders and the price is x.

(a) Is bidding his true value still a dominant strategy for bidder a? Explain briefly.

(b) What is the seller’s expected revenue? Explain briefly.

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