3,155 research outputs found
Descending Price Optimally Coordinates Search
Investigating potential purchases is often a substantial investment under
uncertainty. Standard market designs, such as simultaneous or English auctions,
compound this with uncertainty about the price a bidder will have to pay in
order to win. As a result they tend to confuse the process of search both by
leading to wasteful information acquisition on goods that have already found a
good purchaser and by discouraging needed investigations of objects,
potentially eliminating all gains from trade. In contrast, we show that the
Dutch auction preserves all of its properties from a standard setting without
information costs because it guarantees, at the time of information
acquisition, a price at which the good can be purchased. Calibrations to
start-up acquisition and timber auctions suggest that in practice the social
losses through poor search coordination in standard formats are an order of
magnitude or two larger than the (negligible) inefficiencies arising from
ex-ante bidder asymmetries.Comment: JEL Classification: D44, D47, D82, D83. 117 pages, of which 74 are
appendi
I/O-Efficient Planar Range Skyline and Attrition Priority Queues
In the planar range skyline reporting problem, we store a set P of n 2D
points in a structure such that, given a query rectangle Q = [a_1, a_2] x [b_1,
b_2], the maxima (a.k.a. skyline) of P \cap Q can be reported efficiently. The
query is 3-sided if an edge of Q is grounded, giving rise to two variants:
top-open (b_2 = \infty) and left-open (a_1 = -\infty) queries.
All our results are in external memory under the O(n/B) space budget, for
both the static and dynamic settings:
* For static P, we give structures that answer top-open queries in O(log_B n
+ k/B), O(loglog_B U + k/B), and O(1 + k/B) I/Os when the universe is R^2, a U
x U grid, and a rank space grid [O(n)]^2, respectively (where k is the number
of reported points). The query complexity is optimal in all cases.
* We show that the left-open case is harder, such that any linear-size
structure must incur \Omega((n/B)^e + k/B) I/Os for a query. We show that this
case is as difficult as the general 4-sided queries, for which we give a static
structure with the optimal query cost O((n/B)^e + k/B).
* We give a dynamic structure that supports top-open queries in O(log_2B^e
(n/B) + k/B^1-e) I/Os, and updates in O(log_2B^e (n/B)) I/Os, for any e
satisfying 0 \le e \le 1. This leads to a dynamic structure for 4-sided queries
with optimal query cost O((n/B)^e + k/B), and amortized update cost O(log
(n/B)).
As a contribution of independent interest, we propose an I/O-efficient
version of the fundamental structure priority queue with attrition (PQA). Our
PQA supports FindMin, DeleteMin, and InsertAndAttrite all in O(1) worst case
I/Os, and O(1/B) amortized I/Os per operation.
We also add the new CatenateAndAttrite operation that catenates two PQAs in
O(1) worst case and O(1/B) amortized I/Os. This operation is a non-trivial
extension to the classic PQA of Sundar, even in internal memory.Comment: Appeared at PODS 2013, New York, 19 pages, 10 figures. arXiv admin
note: text overlap with arXiv:1208.4511, arXiv:1207.234
Pandora's Box Problem with Order Constraints
The Pandora's Box Problem, originally formalized by Weitzman in 1979, models
selection from set of random, alternative options, when evaluation is costly.
This includes, for example, the problem of hiring a skilled worker, where only
one hire can be made, but the evaluation of each candidate is an expensive
procedure. Weitzman showed that the Pandora's Box Problem admits an elegant,
simple solution, where the options are considered in decreasing order of
reservation value,i.e., the value that reduces to zero the expected marginal
gain for opening the box. We study for the first time this problem when order -
or precedence - constraints are imposed between the boxes. We show that,
despite the difficulty of defining reservation values for the boxes which take
into account both in-depth and in-breath exploration of the various options,
greedy optimal strategies exist and can be efficiently computed for tree-like
order constraints. We also prove that finding approximately optimal adaptive
search strategies is NP-hard when certain matroid constraints are used to
further restrict the set of boxes which may be opened, or when the order
constraints are given as reachability constraints on a DAG. We complement the
above result by giving approximate adaptive search strategies based on a
connection between optimal adaptive strategies and non-adaptive strategies with
bounded adaptivity gap for a carefully relaxed version of the problem
Optimal allocation of defibrillator drones in mountainous regions
Responding to emergencies in Alpine terrain is quite challenging as air
ambulances and mountain rescue services are often confronted with logistics
challenges and adverse weather conditions that extend the response times
required to provide life-saving support. Among other medical emergencies,
sudden cardiac arrest (SCA) is the most time-sensitive event that requires the
quick provision of medical treatment including cardiopulmonary resuscitation
and electric shocks by automated external defibrillators (AED). An emerging
technology called unmanned aerial vehicles (or drones) is regarded to support
mountain rescuers in overcoming the time criticality of these emergencies by
reducing the time span between SCA and early defibrillation. A drone that is
equipped with a portable AED can fly from a base station to the patient's site
where a bystander receives it and starts treatment. This paper considers such a
response system and proposes an integer linear program to determine the optimal
allocation of drone base stations in a given geographical region. In detail,
the developed model follows the objectives to minimize the number of used
drones and to minimize the average travel times of defibrillator drones
responding to SCA patients. In an example of application, under consideration
of historical helicopter response times, the authors test the developed model
and demonstrate the capability of drones to speed up the delivery of AEDs to
SCA patients. Results indicate that time spans between SCA and early
defibrillation can be reduced by the optimal allocation of drone base stations
in a given geographical region, thus increasing the survival rate of SCA
patients
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives
We study a class of procurement auctions with a budget constraint, where an
auctioneer is interested in buying resources or services from a set of agents.
Ideally, the auctioneer would like to select a subset of the resources so as to
maximize his valuation function, without exceeding a given budget. As the
resources are owned by strategic agents however, our overall goal is to design
mechanisms that are truthful, budget-feasible, and obtain a good approximation
to the optimal value. Budget-feasibility creates additional challenges, making
several approaches inapplicable in this setting. Previous results on
budget-feasible mechanisms have considered mostly monotone valuation functions.
In this work, we mainly focus on symmetric submodular valuations, a prominent
class of non-monotone submodular functions that includes cut functions. We
begin first with a purely algorithmic result, obtaining a
-approximation for maximizing symmetric submodular functions
under a budget constraint. We view this as a standalone result of independent
interest, as it is the best known factor achieved by a deterministic algorithm.
We then proceed to propose truthful, budget feasible mechanisms (both
deterministic and randomized), paying particular attention on the Budgeted Max
Cut problem. Our results significantly improve the known approximation ratios
for these objectives, while establishing polynomial running time for cases
where only exponential mechanisms were known. At the heart of our approach lies
an appropriate combination of local search algorithms with results for monotone
submodular valuations, applied to the derived local optima.Comment: A conference version appears in WINE 201
Paid Placement: Advertising and Search on the Internet
Paid placement, where advertisers bid payments to a search engine to
have their products appear next to keyword search results, has emerged
as a predominant form of advertising on the Internet. This paper studies
a product-di¤erentiation model where consumers are initially
uncertain about the desirability of and valuation for di¤erent
sellers products, and can learn about a seller s product through a
costly search. In equilibrium, a seller bids more for placement when his
product is more relevant for a given keyword, and the paid placement of
sellers by the search engine reveals information about the relevance of
their products. This results in e¢ cient (sequential) search by
consumers and increases total output
Learning Utilities and Equilibria in Non-Truthful Auctions
In non-truthful auctions, agents' utility for a strategy depends on the
strategies of the opponents and also the prior distribution over their private
types; the set of Bayes Nash equilibria generally has an intricate dependence
on the prior. Using the First Price Auction as our main demonstrating example,
we show that samples from the prior with agents
suffice for an algorithm to learn the interim utilities for all monotone
bidding strategies. As a consequence, this number of samples suffice for
learning all approximate equilibria. We give almost matching (up to polylog
factors) lower bound on the sample complexity for learning utilities. We also
consider settings where agents must pay a search cost to discover their own
types. Drawing on a connection between this setting and the first price
auction, discovered recently by Kleinberg et al. (2016), we show that samples suffice for utilities and equilibria to be estimated
in a near welfare-optimal descending auction in this setting. En route, we
improve the sample complexity bound, recently obtained by Guo et al. (2019),
for the Pandora's Box problem, which is a classical model for sequential
consumer search
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