399 research outputs found
User Satisfaction in Competitive Sponsored Search
We present a model of competition between web search algorithms, and study
the impact of such competition on user welfare. In our model, search providers
compete for customers by strategically selecting which search results to
display in response to user queries. Customers, in turn, have private
preferences over search results and will tend to use search engines that are
more likely to display pages satisfying their demands.
Our main question is whether competition between search engines increases the
overall welfare of the users (i.e., the likelihood that a user finds a page of
interest). When search engines derive utility only from customers to whom they
show relevant results, we show that they differentiate their results, and every
equilibrium of the resulting game achieves at least half of the welfare that
could be obtained by a social planner. This bound also applies whenever the
likelihood of selecting a given engine is a convex function of the probability
that a user's demand will be satisfied, which includes natural Markovian models
of user behavior.
On the other hand, when search engines derive utility from all customers
(independent of search result relevance) and the customer demand functions are
not convex, there are instances in which the (unique) equilibrium involves no
differentiation between engines and a high degree of randomness in search
results. This can degrade social welfare by a factor of the square root of N
relative to the social optimum, where N is the number of webpages. These bad
equilibria persist even when search engines can extract only small (but
non-zero) expected revenue from dissatisfied users, and much higher revenue
from satisfied ones
Submodular meets Spectral: Greedy Algorithms for Subset Selection, Sparse Approximation and Dictionary Selection
We study the problem of selecting a subset of k random variables from a large
set, in order to obtain the best linear prediction of another variable of
interest. This problem can be viewed in the context of both feature selection
and sparse approximation. We analyze the performance of widely used greedy
heuristics, using insights from the maximization of submodular functions and
spectral analysis. We introduce the submodularity ratio as a key quantity to
help understand why greedy algorithms perform well even when the variables are
highly correlated. Using our techniques, we obtain the strongest known
approximation guarantees for this problem, both in terms of the submodularity
ratio and the smallest k-sparse eigenvalue of the covariance matrix. We further
demonstrate the wide applicability of our techniques by analyzing greedy
algorithms for the dictionary selection problem, and significantly improve the
previously known guarantees. Our theoretical analysis is complemented by
experiments on real-world and synthetic data sets; the experiments show that
the submodularity ratio is a stronger predictor of the performance of greedy
algorithms than other spectral parameters
Quasi-regular sequences and optimal schedules for security games
We study security games in which a defender commits to a mixed strategy for
protecting a finite set of targets of different values. An attacker, knowing
the defender's strategy, chooses which target to attack and for how long. If
the attacker spends time at a target of value , and if he
leaves before the defender visits the target, his utility is ; if the defender visits before he leaves, his utility is 0. The defender's
goal is to minimize the attacker's utility. The defender's strategy consists of
a schedule for visiting the targets; it takes her unit time to switch between
targets. Such games are a simplified model of a number of real-world scenarios
such as protecting computer networks from intruders, crops from thieves, etc.
We show that optimal defender play for this continuous time security games
reduces to the solution of a combinatorial question regarding the existence of
infinite sequences over a finite alphabet, with the following properties for
each symbol : (1) constitutes a prescribed fraction of the
sequence. (2) The occurrences of are spread apart close to evenly, in that
the ratio of the longest to shortest interval between consecutive occurrences
is bounded by a parameter . We call such sequences -quasi-regular.
We show that, surprisingly, -quasi-regular sequences suffice for optimal
defender play. What is more, even randomized -quasi-regular sequences
suffice for optimality. We show that such sequences always exist, and can be
calculated efficiently.
The question of the least for which deterministic -quasi-regular
sequences exist is fascinating. Using an ergodic theoretical approach, we show
that deterministic -quasi-regular sequences always exist. For
we do not know whether deterministic -quasi-regular sequences always exist.Comment: to appear in Proc. of SODA 201
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