113 research outputs found
Revenue Loss in Shrinking Markets
We analyze the revenue loss due to market shrinkage. Specifically, consider a
simple market with one item for sale and bidders whose values are drawn
from some joint distribution. Suppose that the market shrinks as a single
bidder retires from the market. Suppose furthermore that the value of this
retiring bidder is fixed and always strictly smaller than the values of the
other players. We show that even this slight decrease in competition might
cause a significant fall of a multiplicative factor of
in the revenue that can be obtained by a dominant
strategy ex-post individually rational mechanism.
In particular, our results imply a solution to an open question that was
posed by Dobzinski, Fu, and Kleinberg [STOC'11]
Optimal Auctions for Correlated Buyers with Sampling
Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn
from a correlated distribution, an auction with full knowledge on the
distribution can extract the full social surplus. We study whether this
phenomenon persists when the auctioneer has only incomplete knowledge of the
distribution, represented by a finite family of candidate distributions, and
has sample access to the real distribution. We show that the naive approach
which uses samples to distinguish candidate distributions may fail, whereas an
extended version of the Cr\'emer-McLean auction simultaneously extracts full
social surplus under each candidate distribution. With an algebraic argument,
we give a tight bound on the number of samples needed by this auction, which is
the difference between the number of candidate distributions and the dimension
of the linear space they span
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
Sequential Posted Price Mechanisms with Correlated Valuations
We study the revenue performance of sequential posted price mechanisms and
some natural extensions, for a general setting where the valuations of the
buyers are drawn from a correlated distribution. Sequential posted price
mechanisms are conceptually simple mechanisms that work by proposing a
take-it-or-leave-it offer to each buyer. We apply sequential posted price
mechanisms to single-parameter multi-unit settings in which each buyer demands
only one item and the mechanism can assign the service to at most k of the
buyers. For standard sequential posted price mechanisms, we prove that with the
valuation distribution having finite support, no sequential posted price
mechanism can extract a constant fraction of the optimal expected revenue, even
with unlimited supply. We extend this result to the the case of a continuous
valuation distribution when various standard assumptions hold simultaneously.
In fact, it turns out that the best fraction of the optimal revenue that is
extractable by a sequential posted price mechanism is proportional to ratio of
the highest and lowest possible valuation. We prove that for two simple
generalizations of these mechanisms, a better revenue performance can be
achieved: if the sequential posted price mechanism has for each buyer the
option of either proposing an offer or asking the buyer for its valuation, then
a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d
denotes the degree of dependence of the valuations, ranging from complete
independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we
generalize the sequential posted price mechanisms further, such that the
mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer
that depends on the valuations of all buyers except i's, we prove that a
constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be
extracted.Comment: 29 pages, To appear in WINE 201
A Theoretical Examination of Practical Game Playing: Lookahead Search
Abstract. Lookahead search is perhaps the most natural and widely used game playing strategy. Given the practical importance of the method, the aim of this paper is to provide a theoretical performance examination of lookahead search in a wide variety of applications. To determine a strategy play using lookahead search, each agent predicts multiple levels of possible re-actions to her move (via the use of a search tree), and then chooses the play that optimizes her future payoff accounting for these re-actions. There are several choices of optimization function the agents can choose, where the most appropriate choice of function will depend on the specifics of the actual game- we illustrate this in our examples. Furthermore, the type of search tree chosen by computationally-constrained agent can vary. We focus on the case where agents can evaluate only a bounded number, k, of moves into the future. That is, we use depth k search trees and call this approach k-lookahead search. We apply our method in five well-known settings: industrial organization (Cournot’s model); AdWord auctions; congestion games; valid-utility games and basic-utility games; cost-sharing network design games. We consider two questions. First, what i
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