Composable and Efficient Mechanisms

TL;DR

This paper introduces smooth and weakly smooth mechanisms, demonstrating their efficiency and good equilibrium properties when multiple mechanisms are combined, applicable in various informational settings.

Contribution

It defines smooth and weakly smooth mechanisms, proving their composability and efficiency in multi-mechanism environments under different informational assumptions.

Findings

Smooth mechanisms lead to high-quality outcomes in equilibrium.

Weakly smooth mechanisms are approximately efficient under no-overbidding.

Mechanisms compose well, maintaining efficiency in combined settings.

Abstract

We initiate the study of efficient mechanism design with guaranteed good properties even when players participate in multiple different mechanisms simultaneously or sequentially. We define the class of smooth mechanisms, related to smooth games defined by Roughgarden, that can be thought of as mechanisms that generate approximately market clearing prices. We show that smooth mechanisms result in high quality outcome in equilibrium both in the full information setting and in the Bayesian setting with uncertainty about participants, as well as in learning outcomes. Our main result is to show that such mechanisms compose well: smoothness locally at each mechanism implies efficiency globally. For mechanisms where good performance requires that bidders do not bid above their value, we identify the notion of a weakly smooth mechanism. Weakly smooth mechanisms, such as the Vickrey auction, are approximately efficient under the no-overbidding assumption. Similar to smooth mechanisms, weakly smooth mechanisms behave well in composition, and have high quality outcome in equilibrium (assuming no overbidding) both in the full information setting and in the Bayesian setting, as well as in learning outcomes. In most of the paper we assume participants have quasi-linear valuations. We also extend some of our results to settings where participants have budget constraints.