Auctions for Share-Averse Bidders

We introduce and study share-averse auctions , a class of auctions with allocation externalities, in which items can be allocated to arbitrarily many bidders, but the valuation of each individual bidder decreases as the items get allocated to more other bidders. For single-item auctions where players have incomplete information about each others' valuation, we characterize the truthful mechanism that maximizes the auctioneer's revenue, and analyze it for some interesting cases. We then move beyond single-item auctions, and analyze single-minded combinatorial auctions. We derive sufficient conditions for a truthful allocation in this setting. We also obtain a $\sqrt{m}$-approximation algorithm for maximizing social welfare, which is essentially tight unless P=NP.

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