Unifying Identity-Specific and Financial Externalities in Auction Design

Coexistence of identity-specific and financial externalities among bidders is a salient feature of auctions with buyers who are cross shareholders or competing firms in an oligopoly. This paper unifies these two types of externalities in revenue-maximizing auction design. Our main findings are the following. First, these two types of externalities can be unified through the framework of Myerson (1981). Both affect the winning probabilities through their impact on players' externality-augmented virtual values, while their impact on buyers' payments is reflected by an externality-correcting component for each type of externalities, which equals the respective externalities. These components eliminate strategic bidding that would arise from the existence of externalities. Second, the two types of externalities interact fundamentally through shaping players' virtual values. At the optimum, the player with the highest externality-augmented virtual value wins given that it is positive, otherwise seller physically destroys the item. Financial externalities amplify the impact of the identity-specific externalities on winning probabilities. Third, our approach is applicable to revenue-maximizing auction design with cross shareholding. Fourth, our finding renders an approach for revenue-maximizing auction design with asymmetric financial externalities. Particularly, when seller does not value the object, a revenue-maximizing auction can be obtained from any revenue-maximizing auction for a regular setting without externalities by solely transforming the payments.