Participation and exclusion in auctions

- We compare auctioneer payoffs and revenues due to buyer participation and exclusion.
- An example shows the failure of the Bulow-Klemperer Theorem due to seller valuation.
- Extension of the BK Theorem with a minimum reserve price.
- Extension of the BK Theorem with a minimum buyer participation.
- A new tool is developed to establish new results and for further applications.

We provide extensions of the Bulow and Klemperer (1996) result when the seller has value for the object above the minimum value of the buyers. The result may fail. We show that the seller does better with more participation and some exclusion than the optimal exclusion of buyers of low value types. Some amount of exclusion, which is independent of the number of buyers, in the form of the minimum bid is needed to make participation the dominant method for improving the seller payoff from the auctions. There exists N0, which depends on the seller valuation, such that more participation with no exclusion is dominant if and only if the number of participants exceeds N0.