63,589 research outputs found

    Stochastic Coalitional Better-response Dynamics and Strong Nash Equilibrium

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    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

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    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

    Selfish Network Creation with Non-Uniform Edge Cost

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    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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