63,589 research outputs found
Stochastic Coalitional Better-response Dynamics and Strong Nash Equilibrium
We consider coalition formation among players in an n-player finite strategic
game over infinite horizon. At each time a randomly formed coalition makes a
joint deviation from a current action profile such that at new action profile
all players from the coalition are strictly benefited. Such deviations define a
coalitional better-response (CBR) dynamics that is in general stochastic. The
CBR dynamics either converges to a strong Nash equilibrium or stucks in a
closed cycle. We also assume that at each time a selected coalition makes
mistake in deviation with small probability that add mutations (perturbations)
into CBR dynamics. We prove that all strong Nash equilibria and closed cycles
are stochastically stable, i.e., they are selected by perturbed CBR dynamics as
mutations vanish. Similar statement holds for strict strong Nash equilibrium.
We apply CBR dynamics to the network formation games and we prove that all
strongly stable networks and closed cycles are stochastically stable
Mapping the Curricular Structure and Contents of Network Science Courses
As network science has matured as an established field of research, there are
already a number of courses on this topic developed and offered at various
higher education institutions, often at postgraduate levels. In those courses,
instructors adopted different approaches with different focus areas and
curricular designs. We collected information about 30 existing network science
courses from various online sources, and analyzed the contents of their syllabi
or course schedules. The topics and their curricular sequences were extracted
from the course syllabi/schedules and represented as a directed weighted graph,
which we call the topic network. Community detection in the topic network
revealed seven topic clusters, which matched reasonably with the concept list
previously generated by students and educators through the Network Literacy
initiative. The minimum spanning tree of the topic network revealed typical
flows of curricular contents, starting with examples of networks, moving onto
random networks and small-world networks, then branching off to various
subtopics from there. These results illustrate the current state of consensus
formation (including variations and disagreements) among the network science
community on what should be taught about networks and how, which may also be
informative for K--12 education and informal education.Comment: 17 pages, 11 figures, 2 tables; to appear in Cramer, C. et al.
(eds.), Network Science in Education -- Tools and Techniques for Transforming
Teaching and Learning (Springer, 2017, in press
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A tree formulation for signaling games
We provide a detailed presentation and complete analysis of the sender/receiver Lewis signaling game using a game theory extensive form, decision tree formulation. The analysis employs well established game theory ideas and concepts. We establish the existence of four perfect Bayesian equilibria in this game. We explain which equilibrium is the most likely to prevail. Our explanation provides an essential step for understanding the formation of a language convention. Further, we discuss the informational content of such signals and calibrate a more detailed definition of a true (“correct”) signal in terms of the payoffs of the sender and the receiver
Selfish Network Creation with Non-Uniform Edge Cost
Network creation games investigate complex networks from a game-theoretic
point of view. Based on the original model by Fabrikant et al. [PODC'03] many
variants have been introduced. However, almost all versions have the drawback
that edges are treated uniformly, i.e. every edge has the same cost and that
this common parameter heavily influences the outcomes and the analysis of these
games.
We propose and analyze simple and natural parameter-free network creation
games with non-uniform edge cost. Our models are inspired by social networks
where the cost of forming a link is proportional to the popularity of the
targeted node. Besides results on the complexity of computing a best response
and on various properties of the sequential versions, we show that the most
general version of our model has constant Price of Anarchy. To the best of our
knowledge, this is the first proof of a constant Price of Anarchy for any
network creation game.Comment: To appear at SAGT'1
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