Exclusion in All-Pay Auctions

In a recent paper, Baye, Kovenock, and de Vries (1993) derive a general formula for the seller’s expected revenue in an all-pay auction, where the buyers’ valuations are common knowledge. They use this formula to show that excluding the buyer with the highest valuation sometimes increases the seller’s expected revenue. Lobbying may be modeled as an all-pay auction, and the exclusion result may therefore explain the practice of reducing fields of contestants vying for a political prize. One implication is that a politician may, perversely, exclude the individuals who place the highest value on a political prize. The exclusion result depends critically on the assumption that the politician must award the prize to the highest bidder. We describe an alternate procedure that gives the politician more expected revenue. Although a politician adopting our procedure sometimes increases her expected revenue by excluding potential bidders, she should never exclude the buyer with the highest valuation.