Question

A second-price sealed-bid auction is an auction in which every bidder submits his or her bid to the auctioneer, the auctioneer announces the winner to be the bidder who submits the highest bid, and the winner pays the highest bid among the losers. Is the following statement True, False, or Uncertain? Explain why. Every player has a weakly dominant strategy in second-price auction.

Answer 1

A second-price sealed-bid auction is an auction in which every bidder simulatneously submits his bid to the auctioneer, the auctioneer announces the winner to be the bidder who submits the highest bid, and the winner pays the highest bid among the losers which would be the second highest bid.

This statement is true and this type of auction is also called as the Vickrey auction .

here the bidder who wins gets the bid at the price of the second highest bid.

A weakly dominant strategy is one where the player regardless of what other players decision is earns atleast as high a payoff as in any other case ie even if not strictly it is as good as in any other case.

lets take the case of two players b1 and vi

if b1>vi , we know that vi would be worse off playing any non-winning bid (including vi) than playing any other non-winning bid, and is strictly better than playing any winning bid

ie the payoff of vi is 0

next if b1<vi as long as vi is a non bwinng bid ie not tyhe highest bid , it has a 0 payoff again

but it would be a different case if it has a winning bid where playing this winning bid is as good as playing any other winning bid but it is strictly better than playing a non winning bid

next we see that vi= b1

where the player i receives 0 payoff anyways

so here playing no bid is as good as playing a bid