Multi-Unit Auctions with Synergy

In this note we examine four standard multi-unit sealed-bid auctions in the presence of synergy. The structure of the equilibrium bidding strategy under each rule is quite intuitive. Whether the equilibrium involves "bundle-bidding" or "separating-bidding" strategy depends on the presence of the "exposure problem" and the pressure of "demand reduction" in each case. When the bidders can implicitly coordinate to avoid the "exposure problem" and the pressure of "demand reduction," the equilibrium strategy can be calculated using parallels with unit-demand auctions. However, in the presence of the "exposure problem" well-behaved symmetric equilibria that can be characterized by the first-order condition of bidders' maximization problem may not exist in at least some situations.