Consider a second price auction with 2 bidders, 1 and 2, who have values for the good of 20 and 80, respectively. Each knows what the other bidder's valuation is so there is no uncertainty.

(a) [10 points] Show that choosing a bid equal to one's valuation is a weakly dominant strat- egy for bidder 1.

(b) [10 points] Show that if each bidder plays a weakly dominant strategy, the bidder with the highest value always wins the good

(c) [10 points] Is it a Nash equilibrium for bidder 1 to bid 60 and bidder 2 to bid 80? Which bidder is playing a weakly dominated strategy