Selling in Exclusive Markets: Some Observations on Prior-Free Mechanism Design

We consider prior-free benchmarks in non-matroid settings. In particular, we show that a very desirable benchmark proposed by Hartline and Roughgarden is too strong, in the sense that no truthful mechanism can compete with it even in a very simple non-matroid setting where there are two exclusive markets and the seller can only sell to agents in one of them. On the other hand, we show that there is a mechanism that competes with a symmetrized version of this benchmark. We further investigate the more traditional best fixed price profit benchmark and show that there are mechanisms that compete with it in any downward-closed settings.