Buy-many mechanisms are not much better than item pricing

Multi-item mechanisms can be very complex offering many different randomized bundles to the buyer. Such complexity is thought necessary as revenue gaps between optimal and simple are unbounded. Our work shows these do not apply most natural situations: they require that mechanism overcharges buyer for a bundle while selling individual items at much lower prices. We study maximization under buy-many constraint which allows purchase any number of (randomized) he pleases. show O(log⁡n) times achievable by item pricing, where n items. This holds even with an arbitrarily correlated distribution types arbitrary valuations. Furthermore, no family subexponential description achieve better than logarithmic approximation additive