Manipulation via endowments in auctions with multiple goods

We study manipulation via endowments in a market in an auction setting with multiple goods. In the market, there are buyers whose valuations are their private information, and a seller whose set of endowments is her private information. A social planner, who wants to implement a socially desirable allocation, faces the seller's manipulation via endowments, in addition to buyers' manipulation of misreporting their valuations. We call a mechanism immune to the seller's manipulation via endowments destruction-proof. In general, there exists no mechanism which is destruction-proof, together with strategy-proofness of the buyers, efficiency, and participation. Nevertheless, we find a restricted domain of the buyers' valuation profiles satisfying a new condition called per-capita goods-buyer submodularity. We show that, in this domain, there exists a mechanism which is destruction-proof, together with the above properties. The restriction is likely to be met when each winner's valuation is close to the next-highest valuation. We also provide a relation to monopoly theory, and argue that per-capita goods-buyer submodularity is independent of the standard elasticity argument.