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In mechanism design, for example in the case of a single item auction, we often assume that a socially efficient outcome is to allocate the good to the bidder with the highest valuation of that good. In the case of a sponsored search auction, we want the items (slots on the sponsored search space) to be handed out in such a way that the most valuable slots go to the bidders with the highest valuation of the same slots.

In the sponsored search auction case, whom is the allocation optimal for? The bidders, or the web user, or both? If it is optimal for the web user, why?

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The optimality concept used here is usually Pareto-optimality, a.k.a. Pareto-efficiency.

Pareto efficiency or Pareto optimality is a state of allocation of resources from which it is impossible to reallocate so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off.

So a Pareto-efficient allocation is not necessarily 'optimal for' anyone. It just means that given the current allocation no one can be made better off without cost to others.

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