Bidding-your-valuation is the unique symmetric BNE of the second-price auction (SPA) when bidders have SIPV. However, this is not the unique BNE in a SPA. In fact, there are other asymmetric equilibria that involve bidders using weakly dominated strategies. To show the latter point, consider a SPA with 2 bidders who have Private Values. Sup- pose that bidders' valuations are independent and identically distributed Uniform[0, 1]. Show that bidder 2 bidding $2 regardless of her valuation (i.e., 32(v2) = 2) and bidder 1 bidding $0 regardless of his valuation (i.e., 1(v1) = 0) is also a BNE.