We study the question of collusion in auctions. We start by presenting a model of a first price auction with complete information and direct asymmetric externalities. Following a non-cooperative approach we study the negotiations process which yields a cartel. We show that in the presence of direct externalities the grand coalition may not form, proposing an example of an auction in which a small coalition forms in equilibrium. We continue by studying the stability (in the sense of the core) of coalitions in Bayesian games. We show that all coalitional equilibria can be made incentive compatible. We apply the notion of stability on standard auctions without direct externalities, establishing (mainly) the stability of the grand coalition. With direct externalities and complete information we show that the grand coalition (as well as small coalitions) may become unstable. We conclude by examining the notion of stability in second price auctions with direct externalities and incomplete information. We identify a class of tractable equilibria for these auctions for any given collusion scheme. Finally, in this model, we demonstrate the instability of the grand coalition in the presence of direct externalities, identifying (again) direct externalities as an obstacle to cooperation.
