# Answer to Question #63176 in Microeconomics for Abdu

Question #63176

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.

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.

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