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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.

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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.

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  • $\begingroup$ Interesting, do notions of efficiency for auctions ever consider the seller's utility as well as buyers? (I don't mean revenue maximisation, I mean buyer's and seller's combined utility). In this conversation, they have been referring only to buyers. $\endgroup$
    – Student
    May 12 '20 at 9:31
  • $\begingroup$ @Student: Yes, but mostly in a trivial sense where the seller is assumed to have a zero valuation of the object. $\endgroup$
    – VARulle
    May 12 '20 at 13:16

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