Luofeng Liao, Yuan Gao, Christian Kroer
arXiv 29 Sep 2022 · Econometrics
arXiv:2209.15422 · PDF · DOI · OpenAlex · Extracted main text
Statistical inference under market equilibrium effects has attracted increasing attention recently. In this paper we focus on the specific case of linear Fisher markets. They have been widely use in fair resource allocation of food/blood donations and budget management in large-scale Internet ad auctions. In resource allocation, it is crucial to quantify the variability of the resource received by the agents (such as blood banks and food banks) in addition to fairness and efficiency properties of the systems. For ad auction markets, it is important to establish statistical properties of the platform's revenues in addition to their expected values. To this end, we propose a statistical framework based on the concept of infinite-dimensional Fisher markets. In our framework, we observe a market formed by a finite number of items sampled from an underlying distribution (the "observed market") and aim to infer several important equilibrium quantities of the underlying long-run market. These equilibrium quantities include individual utilities, social welfare, and pacing multipliers. Through the lens of sample average approximation (SSA), we derive a collection of statistical results and show that the observed market provides useful statistical information of the long-run market. In other words, the equilibrium quantities of the observed market converge to the true ones of the long-run market with strong statistical guarantees. These include consistency, finite sample bounds, asymptotics, and confidence. As an extension, we discuss revenue inference in quasilinear Fisher markets.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Vincent Conitzer, Christian Kroer, Debmalya Panigrahi, Okke Schrijve… (2022) Pacing equilibrium in first price auction markets self | 0.843 | 5 | 5 | 60% |
| 2 | Alexander Shapiro (2003) Monte carlo sampling methods | 0.737 | 3 | 3 | 67% |
| 3 | Yuan Gao and Christian Kroer (2022) Infinite-dimensional fisher markets and tractable fair division self | 0.693 | 18 | 11 | 33% |
| 4 | Whitney K Newey and Daniel McFadden (1994) Large sample estimation and hypothesis testing | 0.585 | 4 | 3 | 25% |
| 5 | Alexander Shapiro, Darinka Dentcheva, and Andrzej Ruszczynski (2021) Lectures on stochastic programming: modeling and theory | 0.523 | 7 | 5 | 14% |
| 6 | Martin Aleksandrov, Haris Aziz, Serge Gaspers, and Toby Walsh (2015) Online fair division: Analysing a food bank problem | 0.511 | 3 | 2 | 33% |
| 7 | Richard Cole, Nikhil R Devanur, Vasilis Gkatzelis, Kamal Jain, Tung… (2017) Convex program duality, fisher markets, and Nash social welfare | 0.511 | 3 | 2 | 33% |
| 8 | Sujin Kim, Raghu Pasupathy, and Shane G. Henderson (2015) A Guide to Sample Average Approximation, pages 207–243 | 0.511 | 2 | 2 | 50% |
| 9 | Yossi Azar, Niv Buchbinder, and Kamal Jain (2016) How to allocate goods in an online market? | 0.511 | 2 | 2 | 50% |
| 10 | Lihua Chen, Yinyu Ye, and Jiawei Zhang (2007) A note on equilibrium pricing as convex optimization | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 81 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium | 0.737 | 4 | 2 |
| 2 | Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis | 0.737 | 4 | 4 |