7,371 research outputs found
Multi-Player Diffusion Games on Graph Classes
We study competitive diffusion games on graphs introduced by Alon et al. [1]
to model the spread of influence in social networks. Extending results of
Roshanbin [8] for two players, we investigate the existence of pure Nash
equilibria for at least three players on different classes of graphs including
paths, cycles, grid graphs and hypercubes; as a main contribution, we answer an
open question proving that there is no Nash equilibrium for three players on (m
x n) grids with min(m, n) >= 5. Further, extending results of Etesami and Basar
[3] for two players, we prove the existence of pure Nash equilibria for four
players on every d-dimensional hypercube.Comment: Extended version of the TAMC 2015 conference version now discussing
hypercube results (added details for the proof of Proposition 1
Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data
We consider learning, from strictly behavioral data, the structure and
parameters of linear influence games (LIGs), a class of parametric graphical
games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic
inference (CSI): Making inferences from causal interventions on stable behavior
in strategic settings. Applications include the identification of the most
influential individuals in large (social) networks. Such tasks can also support
policy-making analysis. Motivated by the computational work on LIGs, we cast
the learning problem as maximum-likelihood estimation (MLE) of a generative
model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation
uncovers the fundamental interplay between goodness-of-fit and model
complexity: good models capture equilibrium behavior within the data while
controlling the true number of equilibria, including those unobserved. We
provide a generalization bound establishing the sample complexity for MLE in
our framework. We propose several algorithms including convex loss minimization
(CLM) and sigmoidal approximations. We prove that the number of exact PSNE in
LIGs is small, with high probability; thus, CLM is sound. We illustrate our
approach on synthetic data and real-world U.S. congressional voting records. We
briefly discuss our learning framework's generality and potential applicability
to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending
publication.) Last conference version: submitted March 30, 2012 to UAI 2012.
First conference version: entitled, Learning Influence Games, initially
submitted on June 1, 2010 to NIPS 201
Supercooperation in Evolutionary Games on Correlated Weighted Networks
In this work we study the behavior of classical two-person, two-strategies
evolutionary games on a class of weighted networks derived from
Barab\'asi-Albert and random scale-free unweighted graphs. Using customary
imitative dynamics, our numerical simulation results show that the presence of
link weights that are correlated in a particular manner with the degree of the
link endpoints, leads to unprecedented levels of cooperation in the whole
games' phase space, well above those found for the corresponding unweighted
complex networks. We provide intuitive explanations for this favorable behavior
by transforming the weighted networks into unweighted ones with particular
topological properties. The resulting structures help to understand why
cooperation can thrive and also give ideas as to how such supercooperative
networks might be built.Comment: 21 page
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Nash Equilibria in Reverse Temporal Voronoi Games
We study Voronoi games on temporal graphs as introduced by Boehmer et al.
(IJCAI 2021) where two players each select a vertex in a temporal graph with
the goal of reaching the other vertices earlier than the other player. In this
work, we consider the reverse temporal Voronoi game, that is, a player wants to
maximize the number of vertices reaching her earlier than the other player.
Since temporal distances in temporal graphs are not symmetric in general, this
yields a different game. We investigate the difference between the two games
with respect to the existence of Nash equilibria in various temporal graph
classes including temporal trees, cycles, grids, cliques and split graphs. Our
extensive results show that the two games indeed behave quite differently
depending on the considered temporal graph class
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