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Documents authored by Skopalik, Alexander

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Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.151
Network Investment Games with Wardrop Followers

Authors: Daniel Schmand, Marc Schröder, and Alexander Skopalik

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We study a two-sided network investment game consisting of two sets of players, called providers and users. The game is set in two stages. In the first stage, providers aim to maximize their profit by investing in bandwidth of cloud computing services. The investments of the providers yield a set of usable services for the users. In the second stage, each user wants to process a task and therefore selects a bundle of services so as to minimize the total processing time. We assume the total processing time to be separable over the chosen services and the processing time of each service to depend on the utilization of the service and the installed bandwidth. We provide insights on how competition between providers affects the total costs of the users and show that every game on a series-parallel graph can be reduced to an equivalent single edge game when analyzing the set of subgame perfect Nash equilibria.
Cite as

Daniel Schmand, Marc Schröder, and Alexander Skopalik. Network Investment Games with Wardrop Followers. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 151:1-151:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{schmand_et_al:LIPIcs.ICALP.2019.151,
  author =	{Schmand, Daniel and Schr\"{o}der, Marc and Skopalik, Alexander},
  title =	{{Network Investment Games with Wardrop Followers}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{151:1--151:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.151},
  URN =		{urn:nbn:de:0030-drops-107272},
  doi =		{10.4230/LIPIcs.ICALP.2019.151},
  annote =	{Keywords: Network Investment Game, Wardrop Equilibrium, Subgame Perfect Nash Equilibrium}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.242
Approximate Pure Nash Equilibria in Weighted Congestion Games

Authors: Christoph Hansknecht, Max Klimm, and Alexander Skopalik

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
We study the existence of approximate pure Nash equilibria in weighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically, we show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players we obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions.
Cite as

Christoph Hansknecht, Max Klimm, and Alexander Skopalik. Approximate Pure Nash Equilibria in Weighted Congestion Games. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 242-257, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{hansknecht_et_al:LIPIcs.APPROX-RANDOM.2014.242,
  author =	{Hansknecht, Christoph and Klimm, Max and Skopalik, Alexander},
  title =	{{Approximate Pure Nash Equilibria in Weighted Congestion Games}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{242--257},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.242},
  URN =		{urn:nbn:de:0030-drops-47005},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.242},
  annote =	{Keywords: Congestion game, Pure Nash equilibrium, Approximate equilibrium, Existence, Potential function}
}
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