Robustly Leveraging Collusion in Combinatorial Auctions

Because of its devastating effects in auctions and other mechanisms, collusion is prohibited and legally prosecuted. Yet, colluders have always existed, and may continue to exist. We thus raise the following question for mechanism design: What desiderata are achievable, and by what type of mechanisms, when any set of players who wish to collude are free to do so without any restrictions on the way in which they cooperate and coordinate their actions? In response to this question we put forward and exemplify the notion of a collusion-leveraging mechanism. In essence, this is a mechanism aligning its desiderata with the incentives of all its players, including colluders, to a significant and mutually beneficial extent. Of course such mechanisms may exist only for suitable desiderata. In unrestricted combinatorial auctions, where classical mechanisms essentially guarantee 0 social welfare and 0 revenue in the presence of just two colluders, we prove that it is possible for collusion-leveraging mechanisms to guarantee that the sum of social welfare and revenue is always high, even when all players are collusive. To guarantee better performance, collusion-leveraging mechanisms in essence "welcome" collusive players, rather than pretending they do not exist, raising a host of new questions at the intersection of cooperative and non- cooperative game theory.