Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium

Luofeng Liao, Christian Kroer

Abstract:

The linear Fisher market (LFM) is a basic equi-
011 librium model from economics, which also has
012 application in fair and efficient resource alloca-
013 tion. First-price pacing equilibrium (FPPE) is
014 a model capturing budget-management mecha-
015 nisms in first-price auctions. In certain practi-
016 cal settings such as advertising auctions, there
017 is an interest in performing statistical inference
018 over these models. A popular methodology for
019 general statistical inference is the bootstrap pro-
020 cedure. Yet, for LFM and FPPE there is no ex-
021 isting theory for the valid application of boot-
022 strap procedures. In this paper, we introduce and
023 devise several statistically valid bootstrap infer-
024 ence procedures for LFM and FPPE. The most
025 challenging part is to bootstrap general FPPE,
026 which reduces to bootstrapping constrained M-
027 estimators, a largely unexplored problem. We are
028 able to devise a bootstrap procedure for FPPE
029 under mild degeneracy conditions by using the
030 powerful tool of epi-convergence theory. Exper-
031 iments with synthetic and semi-real data verify
032 our theory.