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.