Question

Suppose you are a bidder in a first-price sealed-bid auction for a single object, where players submit bids simultaneously and the player who bid the highest wins the object and must pay his/her bid. Assume there are two other bidders, so this is a three-player game. You do not observe the valuations of the other bidders, but assume that you believe their valuations are identically and independently distributed according to a uniform distribution on the interval from 0 to 20. Suppose that the other two bidders play the strategy of bidding exactly their valuations. That is, letting bidder j's valuation be v; (wherejis one of the other players), bidder j bids b; = vj.

Answer 1

Solution:
Probability of winning the auction = (x/20)²

As the distributions of other two players are uniformally distributed between 0 and 20.

According to Bayesian Equailibrium equation:

Optimal bid = ((n-1)/n) * 12

= (2/3) * 12

= 8 Answer