462 research outputs found
Pacing Equilibrium in First-Price Auction Markets
In the isolated auction of a single item, second price often dominates first
price in properties of theoretical interest. But, single items are rarely sold
in true isolation, so considering the broader context is critical when adopting
a pricing strategy. In this paper, we study a model centrally relevant to
Internet advertising and show that when items (ad impressions) are individually
auctioned within the context of a larger system that is managing budgets,
theory offers surprising endorsement for using a first price auction to sell
each individual item. In particular, first price auctions offer theoretical
guarantees of equilibrium uniqueness, monotonicity, and other desirable
properties, as well as efficient computability as the solution to the
well-studied Eisenberg-Gale convex program. We also use simulations to
demonstrate that a bidder's incentive to deviate vanishes in thick markets
Vulnerabilities of Single-Round Incentive Compatibility in Auto-bidding: Theory and Evidence from ROI-Constrained Online Advertising Markets
Most of the work in auction design literature assumes that bidders behave
rationally based on the information available for every individual auction, and
the revelation principle enables designers to restrict their efforts to
incentive compatible (IC) mechanisms. However, in today's online advertising
markets, one of the most important real-life applications of auction design,
the data and computational power required to bid optimally are only available
to the auction designer, and an advertiser can only participate by setting
performance objectives and constraints for its proxy auto-bidder provided by
the platform.
The prevalence of auto-bidding necessitates a review of auction theory. In
this paper, we examine properties of auto-bidding markets through the lens of
ROI-constrained value-maximizing campaigns, which are widely adopted in many
global-scale online advertising platforms. Through theoretical analysis and
empirical experiments on both synthetic and realistic data, we find that second
price auction exhibits many undesirable properties (equilibrium multiplicity,
computational hardness, exploitability by bidders and auctioneers, instability
of bidders' utilities, and interference in A/B testing) and loses its dominant
theoretical advantages in single-item scenarios. Some of these phenomena have
been identified in literature (for budget-constrained auto-bidders) and widely
observed in practice, and we show that they are actually deeply rooted in the
property of (single-round) incentive compatibility. Although many complex
designs have been proposed in literature, first and second price auctions
remain popular in industry. We hope that our work could bring new perspectives
to the community and benefit practitioners to attain a better grasp of
real-world markets
Statistical Inference and A/B Testing for First-Price Pacing Equilibria
We initiate the study of statistical inference and A/B testing for
first-price pacing equilibria (FPPE). The FPPE model captures the dynamics
resulting from large-scale first-price auction markets where buyers use
pacing-based budget management. Such markets arise in the context of internet
advertising, where budgets are prevalent.
We propose a statistical framework for the FPPE model, in which a limit FPPE
with a continuum of items models the long-run steady-state behavior of the
auction platform, and an observable FPPE consisting of a finite number of items
provides the data to estimate primitives of the limit FPPE, such as revenue,
Nash social welfare (a fair metric of efficiency), and other parameters of
interest. We develop central limit theorems and asymptotically valid confidence
intervals. Furthermore, we establish the asymptotic local minimax optimality of
our estimators. We then show that the theory can be used for conducting
statistically valid A/B testing on auction platforms. Numerical simulations
verify our central limit theorems, and empirical coverage rates for our
confidence intervals agree with our theory.Comment: - fix referenc
Computing large market equilibria using abstractions
Computing market equilibria is an important practical problem for market
design (e.g. fair division, item allocation). However, computing equilibria
requires large amounts of information (e.g. all valuations for all buyers for
all items) and compute power. We consider ameliorating these issues by applying
a method used for solving complex games: constructing a coarsened abstraction
of a given market, solving for the equilibrium in the abstraction, and lifting
the prices and allocations back to the original market. We show how to bound
important quantities such as regret, envy, Nash social welfare, Pareto
optimality, and maximin share when the abstracted prices and allocations are
used in place of the real equilibrium. We then study two abstraction methods of
interest for practitioners: 1) filling in unknown valuations using techniques
from matrix completion, 2) reducing the problem size by aggregating groups of
buyers/items into smaller numbers of representative buyers/items and solving
for equilibrium in this coarsened market. We find that in real data
allocations/prices that are relatively close to equilibria can be computed from
even very coarse abstractions
Statistical Inference for Fisher Market Equilibrium
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
Contextual Standard Auctions with Budgets: Revenue Equivalence and Efficiency Guarantees
The internet advertising market is a multi-billion dollar industry, in which
advertisers buy thousands of ad placements every day by repeatedly
participating in auctions. In recent years, the industry has shifted to
first-price auctions as the preferred paradigm for selling advertising slots.
Another important and ubiquitous feature of these auctions is the presence of
campaign budgets, which specify the maximum amount the advertisers are willing
to pay over a specified time period. In this paper, we present a new model to
study the equilibrium bidding strategies in standard auctions, a large class of
auctions that includes first- and second-price auctions, for advertisers who
satisfy budget constraints on average. Our model dispenses with the common, yet
unrealistic assumption that advertisers' values are independent and instead
assumes a contextual model in which advertisers determine their values using a
common feature vector. We show the existence of a natural value-pacing-based
Bayes-Nash equilibrium under very mild assumptions. Furthermore, we prove a
revenue equivalence showing that all standard auctions yield the same revenue
even in the presence of budget constraints. Leveraging this equivalence, we
prove Price of Anarchy bounds for liquid welfare and structural properties of
pacing-based equilibria that hold for all standard auctions. Our work takes an
important step toward understanding the implications of the shift to
first-price auctions in internet advertising markets
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