Wikipedia states:
When the auction involves a single item for sale and each participant
has as an independent private value for the item auctioned, the
expected payment and expected revenues of an English auction is
theoretically equivalent to that of the Vickrey auction, and both
mechanisms have weakly dominant strategies.[1] Both the Vickrey and
English auction, although very different procedurally, award the item
to the bidder with the highest value at a price equal to the value of
the second highest bidder.[2]
In an English auction, the object goes to the highest bidder who pays at the price they proposed.
In a Vickrey auction, the object goes to the highest bidder, who pays at the second-highest price.
Given this, how are they "equivalent" to each other? The only thing common between the two, per my understanding, is that the highest bidder always wins.
My guess is that, in an English auction, when the second-highest bidder eventually places a bid (say b0) corresponding to their max affordable value, the highest bidder can place another bid ever so slightly higher (say b1). The object is then sold at b1.
In a Vickrey auction, the highest bidder would pay b0.
Since b0 is almost equal to b1, I imagine that's where the equivalence comes from.
Best Answer
Because in the Vickrey auction, each bidder is bidding their value (since it is a closed auction), whereas in the English open auction, the winning bidder has bid a price just at-or-above the second-highest value (instead of bidding their value which is the highest).