Question

Consider a first-price sealed-bid auction. Suppose bidders' valuations are v1=10 and v2=10. Suppose bidder 2 submits a bid b2=10. Then, in a Nash equilibrium in pure strategies bidder 1 must be submitting a bid equal to ______. In this Nash equilibrium, bidder 1's payoff is equal to ______.

Please explain!!

Answer 1

In a pure stratergy the first bidder value is 10 and second biddr value is 20

V1 = 10

V2 = 20

Bid value of 2nd bidder = 10

According to pure stratergies assume thefirst bidder bid value as i.

if the values of first bidder

B2 i > V1 than the first bidder will loose and pay off is zero

i > b2 > V1 first bidder wins the auction and the pay off is negative and he should avoid bidding

So according tgo this responses the first bidder value B1 = 10 and the payoff is zero as the responses are equally distributted with same probability between 1 and 2