Consider a second price auction with 2 bidders, 1 and 2, who have values for the
ID: 1127887 • Letter: C
Question
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 strategy 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?
Explanation / Answer
ans.a) A weakly dominant strategy is a strategy, if regardless of what any other players do, the strategy earns a player a payoff at least as high as any other strategy, and, the strategy earns a strictly higher payoff for some profile of other players' strategies. In the given auction, bidder 1 has valued the good at 20 and each bidder knows what the other bidders' valuations are. So the strategy is a weakly dominant strategy as bidder 1 will win the bid.