An auction house uses either a first-price or a second-price sealed-bid auction to determine the buyer of a valuable painting among the bidders, and the payment paid by the winning bidder. The winner is the highest bidder in either case. In a first-price auction the winner pays his own bid. In a second-price auction the winner pays the second highest bid (lower or identical to the highest bid). Both of these auctions are strategic games since the sealed bids mean that bids are submitted simultaneously. The particular painting is valued at $2 million by bidder A and at $1 million by bidder B, and they are the only bidders. Assume that bidder A wins if the submitted bids are identical. Determine who can be the winner in an arbitrary Nash-equilibrium when the first-price auction is used, and determine the same when the second-price auction is used. Note that you don't need to identify the Nash-equilibria themselves, just whether both bidders or only one bidder can win in a Nash-equilibrium. how to prove this?