Answer to Question #63176 in Microeconomics for Abdu

Question

Consider the N- bidder auction model. Each bidder's valuation,
Vi, is uniformly distributed on [0, 1], and independent of the other
bidders' valuations, for i = 1,....,N.
i. In the rst price auction, let us focus on strategies of the
form Bi(v) = B(v) = kv for each i, where k is a positive
constant. Show that in a Nash equilibrium where each player
bids according to B(.
), k = ((n-1)/n).
ii. Show that in the second price auction, it is weakly dominant
for each bidder to bid his true valuation, that is, Bi(v) = v.