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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 "strongly decreasing", "weakly decreasing" and "increasing" 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.