Single Object Auctions With Externalities: A Tractable Model

We consider the single object auction model with allocative externalities in a private valuation and quasi-linear setting. We model externalities by assuming that every agent has a private valuation (for the object) and a strict ranking of other agents. The utility for an agent when another agent receives the object is the product of his own valuation and a real number that depends on the rank of this agent in his ranking. When the only private information is the valuation of the agents, we characterise the implementable allocation rules and use these to derive the optimal auction. The optimal auction collects payments from agents who do not receive the object.