Bundling Equilibrium in Combinatorial auctions

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This paper analyzes individually-rational ex post equilibrium in the VC (Vickrey-Clarke) combinatorial auctions. If Σ is a family of bundles of goods, the organizer may restrict the participants by requiring them to submit their bids only for bundles in Σ. The Σ-VC combinatorial auctions (multi-good auctions) obtained in this way are known to be individually-rational truth-telling mechanisms. In contrast, this paper deals with non-restricted VC auctions, in which the buyers restrict themselves to bids on bundles in Σ, because it is rational for them to do so. That is, it may be that when the buyers report their valuation of the bundles in Σ, they are in an equilibrium. We fully characterize those Σ that induce individually rational equilibrium in every VC auction, and we refer to the associated equilibrium as a bundling equilibrium. The number of bundles in Σ represents the communication complexity of the equilibrium. A special case of bundling equilibrium is partition-based equilibrium, in which Σ is a field, that is, it is generated by a partition. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium, focusing in particular on partition-based equilibrium.