  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.
