Exchange mechanisms in the presence of externalities.

Summary We study the issue of collusion in auctions. We begin by presenting a model of first-price auctions under full information and non-symmetric direct externalities. We follow a non-cooperative approach by studying the bargaining process that describes the formation of a cartel. We show that in the presence of direct externalities the formation of the grand coalition is not guaranteed, by proposing an example of an auction in which a small coalition forms in equilibrium. We continue by studying the stability (in the core sense) of coalitions in Bayesian games. We show that any coalitional equilibrium is incentive-free without loss of generality. We thus apply the notion of stability to joint auction procedures without direct externalities, establishing (especially) the stability of the grand coalition. With direct externalities in full information we show that the grand coalition (as well as a smaller coalition) can become unstable. We end by examining the notion of stability in second price auctions with direct externalities in incomplete information. We identify a class of manageable equilibria in these auctions for any given form of collusion. Finally, in this model, we demonstrate the instability of the grand coalition in the presence of direct externalities, again identifying direct externalities as an obstacle to cooperation.