There are three bidders. Bidders 1 and 2 have values v1 and v2 , each of which is random number independently and uniformly distributed on the interval [0,1]. Through having performed the requisite level research, bidder 1 and 2 know their own values for the item, v1 and v2, respectively, but they do not know each other's value for them.

Bidder 3 has not performed enough research to know his own true value for the item. He does not know that he and bidder 2 are extremely similar, ad therefore, that his true value v3 is exactly equal to the true value v2 of bidder 2. The problem is that bidder 3 does not know this value v2 (nor does he know v1 ).

a. How should bidder 1 bid in this auction? How should bidder 2 bid?

b. How should bidder 3 behave in this auction? Provide an explanation for your answer.