# concept of efficiency in auction theory [closed]

I have some confusions about the concept of "efficiency" in auction theory. One interpretation is that an auction is efficient if it maximizes the social-welfare. But social-welfare is not well defined (or if you can point me to a formal definition of social welfare) and its interpretation seems to vary in different scenarios.

Another interpretation of "efficiency" is that an auction is efficient if each item goes to the highest bidder. This one is easy to understand than the first interpretation. But when it comes to multi-unit auctions in which items can also be sold in bundles, this interpretation also puzzles me. For example, consider the following auction. The table lists the valuation of three bidders for two items and their bundle.

            A     B      {A, B}
bidder 1  3     0        0
bidder 2  0     3        0
bidder 3  0     0        5


So in this case, bidder 1 the highest bidder for $A$, bidder 2 is the highest bidder for $B$, and bidder 3 is the highest bidder for package $\{A, B\}$. If we use the first interpretation, then the efficient outcome is to assign $A$ to 1 and assign $B$ to 2; but if we use the second interpretation, assigning $\{A, B\}$ to bidder 3 seems also be efficient, isn't it?

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## closed as off-topic by Ricardo Andrade, Stefan Kohl, Lucia, Yemon Choi, Chris GodsilDec 31 '14 at 13:00

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Ricardo Andrade, Stefan Kohl, Lucia, Yemon Choi, Chris Godsil
If this question can be reworded to fit the rules in the help center, please edit the question.

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