We introduce a class of mechanisms, called bidding dubs, for agents to coordinate their bidding in auctions. In a bidding club agents first conduct a "pre-auction" within the club; depending on the outcome of the pre-auction some subset of the members of the club bid in the primary auction in a prescribed way; and, in some cases, certain monetary transfers take place after the auction. Bidding clubs have self-enforcing collusion properties in the context of second-price auctions. We show that this is still true when multiple auctions take place for substitutable goods, as well as for complementary goods. We also present a bidding club protocol for first-price auctions. Finally, we show cases where bidding clubs have self-enforcing cooperation protocols in arbitrary mechanisms.
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