Monotonic Mechanisms for Selling Multiple Goods

TL;DR

This paper demonstrates that restricting to monotonic selling mechanisms can significantly reduce revenue compared to nonmonotonic mechanisms, with monotonic mechanisms achieving at most a factor of k of the optimal revenue.

Contribution

It shows that monotonic mechanisms can yield negligible revenue compared to the maximum, and provides characterizations and bounds for monotonic and allocation-monotonic mechanisms.

Findings

Monotonic mechanisms can be at most k times the revenue of simple selling methods.

Maximal revenue can be arbitrarily larger than what monotonic mechanisms achieve.

Characterizations of monotonic and allocation-monotonic mechanisms are provided.

Abstract

Maximizing the revenue from selling two or more goods has been shown to require the use of $nonmonotonic$ mechanisms, where a higher-valuation buyer may pay less than a lower-valuation one. Here we show that the restriction to $monotonic$ mechanisms may not just lower the revenue, but may in fact yield only a $negligible$ $fraction$ of the maximal revenue; more precisely, the revenue from monotonic mechanisms is no more than k times the simple revenue obtainable by selling the goods separately, or bundled (where k is the number of goods), whereas the maximal revenue may be arbitrarily larger. We then study the class of monotonic mechanisms and its subclass of allocation-monotonic mechanisms, and obtain useful characterizations and revenue bounds.