Revenue and efficiency in multi-unit uniform-price auctions

- I model the uniform-price auction of several identical units with a reservation price.
- Bidders are symmetric and each bidder submits two different bids.
- I examine the effect of changes in the sellerʼs reservation price on revenue and efficiency.
- Increasing the reservation price will increase both the sellerʼs revenue and efficiency.
- The reservation price effect on efficiency is in contrast to other auction formats.

This paper analyzes efficiency in a uniform-price multi-unit auction with a positive reservation price. I demonstrate that the reservation price is an important policy tool that may increase efficiency (or welfare) in multi-unit uniform-price auctions. I show that the higher the reservation price is, the higher is the sellerʼs revenue and the higher is the efficiency of a final allocation of units that could be attained in a multi-unit uniform-price auction. The reservation price increases the bidderʼs equilibrium strategy in a specific way that is inherent to the uniform-price auction. Thus the reservation price effect on efficiency is in contrast to other auction formats; e.g., the reservation price decreases efficiency in the Vickrey auction and single-unit auctions with symmetric bidders. Therefore the main result can be added to the list of results from mechanism design and auction theory that fail to extend the single-unit/single-dimensional context to the multi-unit/multi-dimensional one.