# 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).