Bounding the Competition Complexity via Dual Flows, Discretizations, and Symmetries

Designing a multi-item auction to extract optimal revenue is very difficult and often practically infeasible, but by recruiting additional buyers to compete for the items, a seller can run a simple auction (such as running a separate second-price auction for each item) and still extract greater revenue than the optimal mechanism without extra buyers. The number of additional bidders necessary such that selling the items separately (to additional bidders) guarantees greater expected revenue than the optimal mechanism (without additional bidders) is termed the competition complexity. Seminal work by Bulow and Klemperer showed that perhaps surprisingly, only one additional buyer is needed in the single-item setting. But with even two independent items, things are more complex; previous work has shown that the competition complexity for n buyers with additive values for two items drawn independently and identically distributed from the equal revenue distribution is Ω(logn) and O( √ n). We seek to close the gap between the currently established upper and lower bounds by exploring a number of different techniques to make this bound tight in n.