8 research outputs found
Robust Market Equilibria with Uncertain Preferences
The problem of allocating scarce items to individuals is an important
practical question in market design. An increasingly popular set of mechanisms
for this task uses the concept of market equilibrium: individuals report their
preferences, have a budget of real or fake currency, and a set of prices for
items and allocations is computed that sets demand equal to supply. An
important real world issue with such mechanisms is that individual valuations
are often only imperfectly known. In this paper, we show how concepts from
classical market equilibrium can be extended to reflect such uncertainty. We
show that in linear, divisible Fisher markets a robust market equilibrium (RME)
always exists; this also holds in settings where buyers may retain unspent
money. We provide theoretical analysis of the allocative properties of RME in
terms of envy and regret. Though RME are hard to compute for general
uncertainty sets, we consider some natural and tractable uncertainty sets which
lead to well behaved formulations of the problem that can be solved via modern
convex programming methods. Finally, we show that very mild uncertainty about
valuations can cause RME allocations to outperform those which take estimates
as having no underlying uncertainty.Comment: Extended preprint of an article accepted to AAAI-20. Contains
supplementary material as appendices. Due to figures, this manuscript is best
printed in colo
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
Implementing Fairness Constraints in Markets Using Taxes and Subsidies
Fisher markets are those where buyers with budgets compete for scarce items,
a natural model for many real world markets including online advertising. A
market equilibrium is a set of prices and allocations of items such that supply
meets demand. We show how market designers can use taxes or subsidies in Fisher
markets to ensure that market equilibrium outcomes fall within certain
constraints. We show how these taxes and subsidies can be computed even in an
online setting where the market designer does not have access to private
valuations. We adapt various types of fairness constraints proposed in existing
literature to the market case and show who benefits and who loses from these
constraints, as well as the extent to which properties of markets including
Pareto optimality, envy-freeness, and incentive compatibility are preserved. We
find that some prior discussed constraints have few guarantees in terms of who
is made better or worse off by their imposition
Practical algorithms and experimentally validated incentives for equilibrium-based fair division (A-CEEI)
Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is an
equilibrium-based solution concept for fair division of discrete items to
agents with combinatorial demands. In theory, it is known that in
asymptotically large markets:
1. For incentives, the A-CEEI mechanism is Envy-Free-but-for-Tie-Breaking
(EF-TB), which implies that it is Strategyproof-in-the-Large (SP-L).
2. From a computational perspective, computing the equilibrium solution is
unfortunately a computationally intractable problem (in the worst-case,
assuming ).
We develop a new heuristic algorithm that outperforms the previous
state-of-the-art by multiple orders of magnitude. This new, faster algorithm
lets us perform experiments on real-world inputs for the first time. We
discover that with real-world preferences, even in a realistic implementation
that satisfies the EF-TB and SP-L properties, agents may have surprisingly
simple and plausible deviations from truthful reporting of preferences. To this
end, we propose a novel strengthening of EF-TB, which dramatically reduces the
potential for strategic deviations from truthful reporting in our experiments.
A (variant of) our algorithm is now in production: on real course allocation
problems it is much faster, has zero clearing error, and has stronger incentive
properties than the prior state-of-the-art implementation.Comment: To appear in EC 202
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