I need help with this question as I'm not sure what I should be doing:
The BNE of a second-price auction is such that every bidder i bids their
exact valuation: bi(vi) = vi , for any vi /in [0,1]. You are asked to verify this fact in the
case of n = 2 bidders whose valuations are independent and uniformly distributed over
the interval [0,1]. To this end, you have to follow the steps below.
1. Given that player 2 bids her exact valuation, the expected payoff of bidder 1 when
she receives the valuation v1 /in [0,1] and bids b is U1(v1; b) = [from 0 to b] (v1 - v2)dv2. v2 = price paid
Give a simple expression for U1(v1, b).
2. Solve the problem max U1(v1, b) and interpret your result.
Any help would be appreciated.
The BNE of a second-price auction is such that every bidder i bids their
exact valuation: bi(vi) = vi , for any vi /in [0,1]. You are asked to verify this fact in the
case of n = 2 bidders whose valuations are independent and uniformly distributed over
the interval [0,1]. To this end, you have to follow the steps below.
1. Given that player 2 bids her exact valuation, the expected payoff of bidder 1 when
she receives the valuation v1 /in [0,1] and bids b is U1(v1; b) = [from 0 to b] (v1 - v2)dv2. v2 = price paid
Give a simple expression for U1(v1, b).
2. Solve the problem max U1(v1, b) and interpret your result.
Any help would be appreciated.