Bidding rings: a bargaining approach

We address the issue of bidder ring formation in single and multi-unit Vickrey auctions. We analyze this issue in a bargaining game set up under the assumption that valuation of bidders is commonly known only amongst themselves. In the single unit case, we show that the equilibrium coalition structure can only be an order preserving r-ring , that includes the winner and the top (r−1)(r−1) losers. In the multiple units case, we specify sufficient conditions for formation of an interesting class of equilibrium coalition structures, which we call single winner ring with free riding, where exactly one winner colludes with all the losers and generates maximum possible bidders' surplus, and, depending on the protocol, the remaining winners free ride either by staying alone or by colluding in pairs.