Simple Bayesian and ex-post equilibria in combinatorial auctions

This paper derives Bayesian equilibria under general conditions for a broad family of sealed-bid combinatorial auction formats under incomplete information. Equilibria are constructed by linking an equilibrium of the combinatorial auction format to an equilibrium of its single-unit version, thereby providing a closed-form expression if the single-unit version has one. Auction formats that share the same single-unit version, like the Vickrey auction and all bidder-optimal core-selecting auctions, have common equilibria for any number of items and bidders. Furthermore, if an ex-post equilibrium exists in the single-unit version of an auction then the auction format has an ex-post equilibrium in the combinatorial auction. We characterize the ex-post equilibria for a subfamily of auctions.