1,389 research outputs found
On Sparse Discretization for Graphical Games
This short paper concerns discretization schemes for representing and
computing approximate Nash equilibria, with emphasis on graphical games, but
briefly touching on normal-form and poly-matrix games. The main technical
contribution is a representation theorem that informally states that to account
for every exact Nash equilibrium using a nearby approximate Nash equilibrium on
a grid over mixed strategies, a uniform discretization size linear on the
inverse of the approximation quality and natural game-representation parameters
suffices. For graphical games, under natural conditions, the discretization is
logarithmic in the game-representation size, a substantial improvement over the
linear dependency previously required. The paper has five other objectives: (1)
given the venue, to highlight the important, but often ignored, role that work
on constraint networks in AI has in simplifying the derivation and analysis of
algorithms for computing approximate Nash equilibria; (2) to summarize the
state-of-the-art on computing approximate Nash equilibria, with emphasis on
relevance to graphical games; (3) to help clarify the distinction between
sparse-discretization and sparse-support techniques; (4) to illustrate and
advocate for the deliberate mathematical simplicity of the formal proof of the
representation theorem; and (5) to list and discuss important open problems,
emphasizing graphical-game generalizations, which the AI community is most
suitable to solve.Comment: 30 pages. Original research note drafted in Dec. 2002 and posted
online Spring'03 (http://www.cis.upenn.
edu/~mkearns/teaching/cgt/revised_approx_bnd.pdf) as part of a course on
computational game theory taught by Prof. Michael Kearns at the University of
Pennsylvania; First major revision sent to WINE'10; Current version sent to
JAIR on April 25, 201
On Influence, Stable Behavior, and the Most Influential Individuals in Networks: A Game-Theoretic Approach
We introduce a new approach to the study of influence in strategic settings
where the action of an individual depends on that of others in a
network-structured way. We propose \emph{influence games} as a
\emph{game-theoretic} model of the behavior of a large but finite networked
population. Influence games allow \emph{both} positive and negative
\emph{influence factors}, permitting reversals in behavioral choices. We
embrace \emph{pure-strategy Nash equilibrium (PSNE)}, an important solution
concept in non-cooperative game theory, to formally define the \emph{stable
outcomes} of an influence game and to predict potential outcomes without
explicitly considering intricate dynamics. We address an important problem in
network influence, the identification of the \emph{most influential
individuals}, and approach it algorithmically using PSNE computation.
\emph{Computationally}, we provide (a) complexity characterizations of various
problems on influence games; (b) efficient algorithms for several special cases
and heuristics for hard cases; and (c) approximation algorithms, with provable
guarantees, for the problem of identifying the most influential individuals.
\emph{Experimentally}, we evaluate our approach using both synthetic influence
games as well as several real-world settings of general interest, each
corresponding to a separate branch of the U.S. Government.
\emph{Mathematically,} we connect influence games to important game-theoretic
models: \emph{potential and polymatrix games}.Comment: Accepted to AI Journal, subject to addressing the reviewers' points
(which are addressed in this version). An earlier version of the article
appeared in AAAI-1
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