714 research outputs found
Evolutionary Poisson Games for Controlling Large Population Behaviors
Emerging applications in engineering such as crowd-sourcing and
(mis)information propagation involve a large population of heterogeneous users
or agents in a complex network who strategically make dynamic decisions. In
this work, we establish an evolutionary Poisson game framework to capture the
random, dynamic and heterogeneous interactions of agents in a holistic fashion,
and design mechanisms to control their behaviors to achieve a system-wide
objective. We use the antivirus protection challenge in cyber security to
motivate the framework, where each user in the network can choose whether or
not to adopt the software. We introduce the notion of evolutionary Poisson
stable equilibrium for the game, and show its existence and uniqueness. Online
algorithms are developed using the techniques of stochastic approximation
coupled with the population dynamics, and they are shown to converge to the
optimal solution of the controller problem. Numerical examples are used to
illustrate and corroborate our results
Data-Driven Estimation in Equilibrium Using Inverse Optimization
Equilibrium modeling is common in a variety of fields such as game theory and
transportation science. The inputs for these models, however, are often
difficult to estimate, while their outputs, i.e., the equilibria they are meant
to describe, are often directly observable. By combining ideas from inverse
optimization with the theory of variational inequalities, we develop an
efficient, data-driven technique for estimating the parameters of these models
from observed equilibria. We use this technique to estimate the utility
functions of players in a game from their observed actions and to estimate the
congestion function on a road network from traffic count data. A distinguishing
feature of our approach is that it supports both parametric and
\emph{nonparametric} estimation by leveraging ideas from statistical learning
(kernel methods and regularization operators). In computational experiments
involving Nash and Wardrop equilibria in a nonparametric setting, we find that
a) we effectively estimate the unknown demand or congestion function,
respectively, and b) our proposed regularization technique substantially
improves the out-of-sample performance of our estimators.Comment: 36 pages, 5 figures Additional theorems for generalization guarantees
and statistical analysis adde
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
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