Efficiency in Auctions Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution.
There are 2 intuitive notions of (ex-post) efficiency: Pareto efficiency and the notion of efficiency that the bidder with the highest value receives the object.

Are the two ever equivalent? I can see that the second notion implies Pareto efficiency, but not the converse.
If bidders have quasilinear preferences and monetary transfers are possible, then the two notions are equivalent: If $x$ is an allocation of the object and $t$ is a vector of monetary transfers with a balanced budget (so the sum of all transfers is 0), then the pair $(x,t)$ is Pareto efficient if and only if $x$ is the utilitarian allocation (object goes to the bidder with the highest valuation).

If monetary transfers are not possible, every allocation of the object to some bidder is Pareto efficient.