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2 bidders have identical valuations of an object for sale. The value of the object is either 0; 50 or 100, with equal probabilities. The object is allocated to one of the bidders in a second price (Vickrey) auction: the highest bidder gets the object and pays the second highest bid.
In case of a tie the object goes to bidder 1. Bidder 1 gets the signal 1 where T1(0) = l; T1 (50) = m and T1(100) = h. Bidder 2 gets the signal T2 where T2 (0) = L and T2(50) = T2(100) = H.
(i) Find a Nash equilibrium of this auction.
(ii) What is the seller's revenue? Could the seller get a higher revenue if bidder 2 had better information? Explain.
Consider the linear transformation (a) Find the image of (3 , -2 , 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transf
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