2 Search Results for "Schröder, Marc"

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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.

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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-dev.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.CSL.2011.5

Power-Set Functors and Saturated Trees

Authors: Jiri Adamek, Stefan Milius, Lawrence S. Moss, and Lurdes Sousa

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Abstract

We combine ideas coming from several fields, including modal logic, coalgebra, and set theory. Modally saturated trees were introduced by K. Fine in 1975. We give a new purely combinatorial formulation of modally saturated trees, and we prove that they form the limit of the final omega-op-chain of the finite power-set functor Pf. From that, we derive an alternative proof of J. Worrell's description of the final coalgebra as the coalgebra of all strongly extensional, finitely branching trees. In the other direction, we represent the final coalgebra for Pf in terms of certain maximal consistent sets in the modal logic K. We also generalize Worrell's result to M-labeled trees for a commutative monoid M, yielding a final coalgebra for the corresponding functor Mf studied by H. P. Gumm and T. Schröder. We introduce the concept of an i-saturated tree for all ordinals i, and then prove that the i-th step in the final chain of the power set functor consists of all i-saturated trees. This leads to a new description of the final coalgebra for the restricted power-set functors Plambda (of subsets of cardinality smaller than lambda).

Cite as

Jiri Adamek, Stefan Milius, Lawrence S. Moss, and Lurdes Sousa. Power-Set Functors and Saturated Trees. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 5-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{adamek_et_al:LIPIcs.CSL.2011.5,
  author =	{Adamek, Jiri and Milius, Stefan and Moss, Lawrence S. and Sousa, Lurdes},
  title =	{{Power-Set Functors and Saturated  Trees}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{5--19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.5},
  URN =		{urn:nbn:de:0030-drops-32194},
  doi =		{10.4230/LIPIcs.CSL.2011.5},
  annote =	{Keywords: saturated tree, extensional tree, final coalgebra, power-set functor, modal logic}
}

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2 Search Results for "Schröder, Marc"

Network Investment Games with Wardrop Followers

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Power-Set Functors and Saturated Trees

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