2,213 research outputs found
Envy Freedom and Prior-free Mechanism Design
We consider the provision of an abstract service to single-dimensional
agents. Our model includes position auctions, single-minded combinatorial
auctions, and constrained matching markets. When the agents' values are drawn
from a distribution, the Bayesian optimal mechanism is given by Myerson (1981)
as a virtual-surplus optimizer. We develop a framework for prior-free mechanism
design and analysis. A good mechanism in our framework approximates the optimal
mechanism for the distribution if there is a distribution; moreover, when there
is no distribution this mechanism still performs well.
We define and characterize optimal envy-free outcomes in symmetric
single-dimensional environments. Our characterization mirrors Myerson's theory.
Furthermore, unlike in mechanism design where there is no point-wise optimal
mechanism, there is always a point-wise optimal envy-free outcome.
Envy-free outcomes and incentive-compatible mechanisms are similar in
structure and performance. We therefore use the optimal envy-free revenue as a
benchmark for measuring the performance of a prior-free mechanism. A good
mechanism is one that approximates the envy free benchmark on any profile of
agent values. We show that good mechanisms exist, and in particular, a natural
generalization of the random sampling auction of Goldberg et al. (2001) is a
constant approximation
Bayesian Incentive Compatibility via Fractional Assignments
Very recently, Hartline and Lucier studied single-parameter mechanism design
problems in the Bayesian setting. They proposed a black-box reduction that
converted Bayesian approximation algorithms into Bayesian-Incentive-Compatible
(BIC) mechanisms while preserving social welfare. It remains a major open
question if one can find similar reduction in the more important
multi-parameter setting. In this paper, we give positive answer to this
question when the prior distribution has finite and small support. We propose a
black-box reduction for designing BIC multi-parameter mechanisms. The reduction
converts any algorithm into an eps-BIC mechanism with only marginal loss in
social welfare. As a result, for combinatorial auctions with sub-additive
agents we get an eps-BIC mechanism that achieves constant approximation.Comment: 22 pages, 1 figur
Mechanisms for Risk Averse Agents, Without Loss
Auctions in which agents' payoffs are random variables have received
increased attention in recent years. In particular, recent work in algorithmic
mechanism design has produced mechanisms employing internal randomization,
partly in response to limitations on deterministic mechanisms imposed by
computational complexity. For many of these mechanisms, which are often
referred to as truthful-in-expectation, incentive compatibility is contingent
on the assumption that agents are risk-neutral. These mechanisms have been
criticized on the grounds that this assumption is too strong, because "real"
agents are typically risk averse, and moreover their precise attitude towards
risk is typically unknown a-priori. In response, researchers in algorithmic
mechanism design have sought the design of universally-truthful mechanisms ---
mechanisms for which incentive-compatibility makes no assumptions regarding
agents' attitudes towards risk.
We show that any truthful-in-expectation mechanism can be generically
transformed into a mechanism that is incentive compatible even when agents are
risk averse, without modifying the mechanism's allocation rule. The transformed
mechanism does not require reporting of agents' risk profiles. Equivalently,
our result can be stated as follows: Every (randomized) allocation rule that is
implementable in dominant strategies when players are risk neutral is also
implementable when players are endowed with an arbitrary and unknown concave
utility function for money.Comment: Presented at the workshop on risk aversion in algorithmic game theory
and mechanism design, held in conjunction with EC 201
Public projects, Boolean functions and the borders of Border's theorem
Border's theorem gives an intuitive linear characterization of the feasible
interim allocation rules of a Bayesian single-item environment, and it has
several applications in economic and algorithmic mechanism design. All known
generalizations of Border's theorem either restrict attention to relatively
simple settings, or resort to approximation. This paper identifies a
complexity-theoretic barrier that indicates, assuming standard complexity class
separations, that Border's theorem cannot be extended significantly beyond the
state-of-the-art. We also identify a surprisingly tight connection between
Myerson's optimal auction theory, when applied to public project settings, and
some fundamental results in the analysis of Boolean functions.Comment: Accepted to ACM EC 201
Near-Optimal and Robust Mechanism Design for Covering Problems with Correlated Players
We consider the problem of designing incentive-compatible, ex-post
individually rational (IR) mechanisms for covering problems in the Bayesian
setting, where players' types are drawn from an underlying distribution and may
be correlated, and the goal is to minimize the expected total payment made by
the mechanism. We formulate a notion of incentive compatibility (IC) that we
call {\em support-based IC} that is substantially more robust than Bayesian IC,
and develop black-box reductions from support-based-IC mechanism design to
algorithm design. For single-dimensional settings, this black-box reduction
applies even when we only have an LP-relative {\em approximation algorithm} for
the algorithmic problem. Thus, we obtain near-optimal mechanisms for various
covering settings including single-dimensional covering problems, multi-item
procurement auctions, and multidimensional facility location.Comment: Major changes compared to the previous version. Please consult this
versio
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
- …