4 Search Results for "Schmand, Daniel"


Document
Threshold Testing and Semi-Online Prophet Inequalities

Authors: Martin Hoefer and Kevin Schewior

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We study threshold testing, an elementary probing model with the goal to choose a large value out of n i.i.d. random variables. An algorithm can test each variable X_i once for some threshold t_i, and the test returns binary feedback whether X_i ≥ t_i or not. Thresholds can be chosen adaptively or non-adaptively by the algorithm. Given the results for the tests of each variable, we then select the variable with highest conditional expectation. We compare the expected value obtained by the testing algorithm with expected maximum of the variables. Threshold testing is a semi-online variant of the gambler’s problem and prophet inequalities. Indeed, the optimal performance of non-adaptive algorithms for threshold testing is governed by the standard i.i.d. prophet inequality of approximately 0.745 + o(1) as n → ∞. We show how adaptive algorithms can significantly improve upon this ratio. Our adaptive testing strategy guarantees a competitive ratio of at least 0.869 - o(1). Moreover, we show that there are distributions that admit only a constant ratio c < 1, even when n → ∞. Finally, when each box can be tested multiple times (with n tests in total), we design an algorithm that achieves a ratio of 1 - o(1).

Cite as

Martin Hoefer and Kevin Schewior. Threshold Testing and Semi-Online Prophet Inequalities. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 62:1-62:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hoefer_et_al:LIPIcs.ESA.2023.62,
  author =	{Hoefer, Martin and Schewior, Kevin},
  title =	{{Threshold Testing and Semi-Online Prophet Inequalities}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{62:1--62:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.62},
  URN =		{urn:nbn:de:0030-drops-187159},
  doi =		{10.4230/LIPIcs.ESA.2023.62},
  annote =	{Keywords: Prophet Inequalities, Testing, Stochastic Probing}
}
Document
Strategic Payments in Financial Networks

Authors: Nils Bertschinger, Martin Hoefer, and Daniel Schmand

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


Abstract
In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of Ω(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems.

Cite as

Nils Bertschinger, Martin Hoefer, and Daniel Schmand. Strategic Payments in Financial Networks. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 46:1-46:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bertschinger_et_al:LIPIcs.ITCS.2020.46,
  author =	{Bertschinger, Nils and Hoefer, Martin and Schmand, Daniel},
  title =	{{Strategic Payments in Financial Networks}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{46:1--46:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.46},
  URN =		{urn:nbn:de:0030-drops-117316},
  doi =		{10.4230/LIPIcs.ITCS.2020.46},
  annote =	{Keywords: Nash Equilibrium, Financial Network, Systemic Risk, Price of Anarchy, Equilibrium Computation}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
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
Competitive Packet Routing with Priority Lists

Authors: Tobias Harks, Britta Peis, Daniel Schmand, and Laura Vargas Koch

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)


Abstract
In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.

Cite as

Tobias Harks, Britta Peis, Daniel Schmand, and Laura Vargas Koch. Competitive Packet Routing with Priority Lists. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 49:1-49:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)


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@InProceedings{harks_et_al:LIPIcs.MFCS.2016.49,
  author =	{Harks, Tobias and Peis, Britta and Schmand, Daniel and Vargas Koch, Laura},
  title =	{{Competitive Packet Routing with Priority Lists}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{49:1--49:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.49},
  URN =		{urn:nbn:de:0030-drops-64622},
  doi =		{10.4230/LIPIcs.MFCS.2016.49},
  annote =	{Keywords: packet routing, Nash equilibrium, price of anarchy, priority policy, complexity}
}
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