PLEASE HOW TO THINK ABOUT IT AND SOLVE

Consider a second-price sealed-bid auction of a single object with two bidders. Both bidders have the same value v for the object. Bidder 1 knows the exact value of v while bidder 2 knows only that v is uniformly distributed on [0,1]. (a) Identify all weakly dominated strategies for each player. Note that a strategy for bidder 1 consists of a bid b(v) for each v[0,1], while a strategy for bidder 2 consists only of a single bid b. We say that a strategy is weakly dominated for bidder 1 if there is some v[0,1] for which the bid b(v) is weakly dominated. Solution: Since bidder 1 knows the value, bidding b(v)=v weakly dominates every other strategy. For bidder 2, any bid b>1 is weakly dominated by b=1; no bid b[0,1] is weakly dominated. (b) Find all Nash equilibria in which neither bidder uses a weakly dominated strategy. Solution: By part (a), bidder 1 must use the strategy b(v)=v. Given this strategy, bidder 2 is indifferent among all bids b[0,1]: whenever he wins the auction, he pays exactly his value and receives a payoff of 0 . Therefore, there is a Nash equilibrium for each b[0,1] given by bidder 1 bidding b(v)=v and bidder 2 bidding b