Efficiency Guarantees from Data

TL;DR

This paper introduces a data-dependent measure of efficiency in game-theoretic outcomes, specifically in auctions, which improves upon traditional worst-case bounds by leveraging observed strategic behavior.

Contribution

It proposes a novel data-dependent framework for bounding efficiency in auctions that is robust to errors and does not require inferring private information.

Findings

Empirical bounds on auction efficiency are significantly tighter than worst-case bounds.

The approach is robust to statistical errors and model mis-specification.

Application to real auction data demonstrates practical effectiveness.

Abstract

Analysis of efficiency of outcomes in game theoretic settings has been a main item of study at the intersection of economics and computer science. The notion of the price of anarchy takes a worst-case stance to efficiency analysis, considering instance independent guarantees of efficiency. We propose a data-dependent analog of the price of anarchy that refines this worst-case assuming access to samples of strategic behavior. We focus on auction settings, where the latter is non-trivial due to the private information held by participants. Our approach to bounding the efficiency from data is robust to statistical errors and mis-specification. Unlike traditional econometrics, which seek to learn the private information of players from observed behavior and then analyze properties of the outcome, we directly quantify the inefficiency without going through the private information. We apply our approach to datasets from a sponsored search auction system and find empirical results that are a significant improvement over bounds from worst-case analysis.