Competition in a multi-unit auction is measured both by the number of bidders and by the relative size of their demands, compared to the number of units on sale. For the same degree of competition (identical aggregate demand and supply), we can observe different demand structures. Do they have an impact on the auction efficiency and revenue-raising properties? It is essential to understand better the impact of competition structure on performance in order to draw recommendations for the design of multi-unit auctions. Theoretical results demonstrate on a simple case contrasting a uniform-price auction of two bidders with a demand of 6 units each, and an auction of 6 bidders with a demand of two units each, that there are multiple equilibria leading to different performance outcome. Experiments are conducted to compare the performance of these two auctions. Results support that with a constant competition degree, the seller gets higher expected revenue with a lower variance when he faces a large number of bidders with small individual demands. We show that this result is attained with no significant effect on allocative efficiency.

Eventing is a three-phased discipline with a stratified progressive performance structure. Sample data (10%) were analysed from all horses competing within the UK (n = 53 890) during 2003 at all five levels of competition (intro, pre-novice, novice, intermediate, advanced). Five performance penalty score contributors were examined (dressage score, show jumping time faults, show jumping jump faults, cross-country jumping faults and cross-country time faults – independent variables) with regard to their effect on final ranking in competition (dependent variable). Percentage accruement of penalty points showed dressage to be the largest contributor (69%) at the intro level, falling to 53% at the advanced level. The show jumping phase was the smallest percentage contributor (greatest influence seen at the novice level, 9%). The influence of cross-country increased as the level of competition became more difficult (greatest at the advanced level, 42%). Linear regression analysis was undertaken with the use of a standardized linear model. The models accounted for between 75 and 83% of all variance dependent on level. Accession of data to the model was almost identical from novice level upwards, with cross-country time and dressage faults exerting the greatest influence. At the lower levels of competition a more complex picture of accession was observed. The use of regression analysis supported the stated sporting aims of eventings governing bodies.