Auctions With Type-Dependent and Negative Externalities : The Optimal Mechanism

We analyze optimal auction design in the presence of negative externalities. We assume that externalities are a function of both the valuation of the agent who suffers it and the valuation of the agent who obtains the good. This introduces two different sources of countervailing incentives: the reservation utility of each bidder becomes type-dependent and the equilibrium utility is not necessarily increasing in the agent's valuation. We characterize the properties of the optimal mechanism when externalities are quot;strongly decreasingquot;, quot;weakly decreasingquot; and quot;increasingquot; in the agent's valuation. Last, we discuss its implementation with sealed-bid auctions. Interestingly, bidding strategies are not necessarily increasing in valuations, and the optimal mechanism can be implemented by setting a price ceiling instead of a reserve price