1,597 research outputs found
Information Aggregation in Exponential Family Markets
We consider the design of prediction market mechanisms known as automated
market makers. We show that we can design these mechanisms via the mold of
\emph{exponential family distributions}, a popular and well-studied probability
distribution template used in statistics. We give a full development of this
relationship and explore a range of benefits. We draw connections between the
information aggregation of market prices and the belief aggregation of learning
agents that rely on exponential family distributions. We develop a very natural
analysis of the market behavior as well as the price equilibrium under the
assumption that the traders exhibit risk aversion according to exponential
utility. We also consider similar aspects under alternative models, such as
when traders are budget constrained
Optimal Single-Choice Prophet Inequalities from Samples
We study the single-choice Prophet Inequality problem when the gambler is
given access to samples. We show that the optimal competitive ratio of
can be achieved with a single sample from each distribution. When the
distributions are identical, we show that for any constant ,
samples from the distribution suffice to achieve the optimal competitive
ratio () within , resolving an open problem of
Correa, D\"utting, Fischer, and Schewior.Comment: Appears in Innovations in Theoretical Computer Science (ITCS) 202
Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms
We study revenue maximization through sequential posted-price (SPP)
mechanisms in single-dimensional settings with buyers and independent but
not necessarily identical value distributions. We construct the SPP mechanisms
by considering the best of two simple pricing rules: one that imitates the
revenue optimal mchanism, namely the Myersonian mechanism, via the taxation
principle and the other that posts a uniform price. Our pricing rules are
rather generalizable and yield the first improvement over long-established
approximation factors in several settings. We design factor-revealing
mathematical programs that crisply capture the approximation factor of our SPP
mechanism. In the single-unit setting, our SPP mechanism yields a better
approximation factor than the state of the art prior to our work (Azar,
Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields
the first improved approximation factor over the state of the art after over
nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP
mechanisms immediately imply improved performance guarantees for the equivalent
free-order prophet inequality problem. In the position auction setting, our SPP
mechanism yields the first higher-than approximation factor. In eager
second-price (ESP) auctions, our two simple pricing rules lead to the first
improved approximation factor that is strictly greater than what is obtained by
the SPP mechanism in the single-unit setting.Comment: Accepted to Operations Researc
Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned
Optimal mechanism design enjoys a beautiful and well-developed theory, and
also a number of killer applications. Rules of thumb produced by the field
influence everything from how governments sell wireless spectrum licenses to
how the major search engines auction off online advertising. There are,
however, some basic problems for which the traditional optimal mechanism design
approach is ill-suited --- either because it makes overly strong assumptions,
or because it advocates overly complex designs. The thesis of this paper is
that approximately optimal mechanisms allow us to reason about fundamental
questions that seem out of reach of the traditional theory.
This survey has three main parts. The first part describes the approximately
optimal mechanism design paradigm --- how it works, and what we aim to learn by
applying it. The second and third parts of the survey cover two case studies,
where we instantiate the general design paradigm to investigate two basic
questions. In the first example, we consider revenue maximization in a
single-item auction with heterogeneous bidders. Our goal is to understand if
complexity --- in the sense of detailed distributional knowledge --- is an
essential feature of good auctions for this problem, or alternatively if there
are simpler auctions that are near-optimal. The second example considers
welfare maximization with multiple items. Our goal here is similar in spirit:
when is complexity --- in the form of high-dimensional bid spaces --- an
essential feature of every auction that guarantees reasonable welfare? Are
there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on
Economics and Computation (EC), June 201
Optimal Algorithm for Bayesian Incentive-Compatible Exploration
We consider a social planner faced with a stream of myopic selfish agents.
The goal of the social planner is to maximize the social welfare, however, it
is limited to using only information asymmetry (regarding previous outcomes)
and cannot use any monetary incentives. The planner recommends actions to
agents, but her recommendations need to be Bayesian Incentive Compatible to be
followed by the agents. Our main result is an optimal algorithm for the
planner, in the case that the actions realizations are deterministic and have
limited support, making significant important progress on this open problem.
Our optimal protocol has two interesting features. First, it always completes
the exploration of a priori more beneficial actions before exploring a priori
less beneficial actions. Second, the randomization in the protocol is
correlated across agents and actions (and not independent at each decision
time).Comment: EC 201
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