Collusion via signalling in simultaneous ascending bid auctions with heterogeneous objects, with and without complementarities

Collusive equilibria exist in simultaneous ascending bid auctions with multiple objects, even with large complementarities in the buyers' utility functions. The bidders collude by dividing the objects among themselves, while keeping the prices low. In the most collusive equilibrium the complementarities are never realized. The scope for collusion however narrows as the ratio between the number of bidders and the number of objects increases.