4 Search Results for "Melissourgos, Themistoklis"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.9
ε-Stationary Nash Equilibria in Multi-Player Stochastic Graph Games

Authors: Ali Asadi, Léonard Brice, Krishnendu Chatterjee, and K. S. Thejaswini

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an ε-Nash equilibrium if no player can gain more than ε by unilaterally deviating from their strategy. In this work, we use ε-Nash equilibria to approximate the computation of Nash equilibria. Specifically, we focus on turn-based, multiplayer stochastic games played on graphs, where players are restricted to stationary strategies - strategies that use randomness but not memory. The problem of deciding the constrained existence of stationary Nash equilibria - where each player’s payoff must lie within a given interval - is known to be ∃ℝ-complete in such a setting (Hansen and Sølvsten, 2020). We extend this line of work to stationary ε-Nash equilibria and present an algorithm that solves the following promise problem: given a game with a Nash equilibrium satisfying the constraints, compute an ε-Nash equilibrium that ε-satisfies those same constraints - satisfies the constraints up to an ε additive error. Our algorithm runs in FNP^NP time. To achieve this, we first show that if a constrained Nash equilibrium exists, then one exists where the non-zero probabilities are at least an inverse of a double-exponential in the input. We further prove that such a strategy can be encoded using floating-point representations, as in the work of Frederiksen and Miltersen (2013), which finally gives us our FNP^NP algorithm. We further show that the decision version of the promise problem is NP-hard. Finally, we show a partial tightness result by proving a lower bound for such techniques: if a constrained Nash equilibrium exists, then there must be one where the probabilities in the strategies are double-exponentially small.
Cite as

Ali Asadi, Léonard Brice, Krishnendu Chatterjee, and K. S. Thejaswini. ε-Stationary Nash Equilibria in Multi-Player Stochastic Graph Games. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{asadi_et_al:LIPIcs.FSTTCS.2025.9,
  author =	{Asadi, Ali and Brice, L\'{e}onard and Chatterjee, Krishnendu and Thejaswini, K. S.},
  title =	{{\epsilon-Stationary Nash Equilibria in Multi-Player Stochastic Graph Games}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.9},
  URN =		{urn:nbn:de:0030-drops-250897},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.9},
  annote =	{Keywords: Nash Equilibria, \epsilon-Nash equilibria, Approximation, Existential Theory of Reals}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.115
Smoothed Analysis of Online Metric Problems

Authors: Christian Coester and Jack Umenberger

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We study three classical online problems - k-server, k-taxi, and chasing size k sets - through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between worst-case and average-case models. Specifically, we show that if the metric space is contained in a ball in any normed space and requests are drawn from distributions whose density functions are upper bounded by 1/σ times the uniform density over the ball, then all three problems admit polylog(k/σ)-competitive algorithms. Our approach is simple: it reduces smoothed instances to fully adversarial instances on finite metrics and leverages existing algorithms in a black-box manner. We also provide a lower bound showing that no algorithm can achieve a competitive ratio sub-polylogarithmic in k/σ, matching our upper bounds up to the exponent of the polylogarithm. In contrast, the best known competitive ratios for these problems in the fully adversarial setting are 2k-1, ∞ and Θ(k²), respectively.
Cite as

Christian Coester and Jack Umenberger. Smoothed Analysis of Online Metric Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 115:1-115:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{coester_et_al:LIPIcs.ESA.2025.115,
  author =	{Coester, Christian and Umenberger, Jack},
  title =	{{Smoothed Analysis of Online Metric Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{115:1--115:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.115},
  URN =		{urn:nbn:de:0030-drops-245847},
  doi =		{10.4230/LIPIcs.ESA.2025.115},
  annote =	{Keywords: Online Algorithms, Competitive Analysis, Smoothed Analysis, k-server, k-taxi, Metrical Service Systems}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.72
On the Smoothed Complexity of Combinatorial Local Search

Authors: Yiannis Giannakopoulos, Alexander Grosz, and Themistoklis Melissourgos

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to identify key structural properties, and corresponding parameters, that determine the smoothed running time of local search dynamics. We formalize this via a black-box tool that provides concrete bounds on the expected maximum number of steps needed until local search reaches an exact local optimum. This bound is particularly strong, in the sense that it holds for any starting feasible solution, any choice of pivoting rule, and does not rely on the choice of specific noise distributions that are applied on the input, but it is parameterized by just a global upper bound ϕ on the probability density. The power of this tool can be demonstrated by instantiating it for various PLS-hard problems of interest to derive efficient smoothed running times (as a function of ϕ and the input size). Most notably, we focus on the important local optimization problem of finding pure Nash equilibria in Congestion Games, that has not been studied before from a smoothed analysis perspective. Specifically, we propose novel smoothed analysis models for general and Network Congestion Games, under various representations, including explicit, step-function, and polynomial resource latencies. We study PLS-hard instances of these problems and show that their standard local search algorithms run in polynomial smoothed time. Further applications of our framework to a wide range of additional combinatorial problems can be found in the full version of our paper.
Cite as

Yiannis Giannakopoulos, Alexander Grosz, and Themistoklis Melissourgos. On the Smoothed Complexity of Combinatorial Local Search. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{giannakopoulos_et_al:LIPIcs.ICALP.2024.72,
  author =	{Giannakopoulos, Yiannis and Grosz, Alexander and Melissourgos, Themistoklis},
  title =	{{On the Smoothed Complexity of Combinatorial Local Search}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{72:1--72:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.72},
  URN =		{urn:nbn:de:0030-drops-202154},
  doi =		{10.4230/LIPIcs.ICALP.2024.72},
  annote =	{Keywords: Smoothed Analysis, local search, better-response dynamics, PLS-hardness, combinatorial local optimization, congestion games, pure Nash equilibria}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.138
Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem

Authors: Argyrios Deligkas, John Fearnley, Themistoklis Melissourgos, and Paul G. Spirakis

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

Abstract
We study the problem of finding an exact solution to the consensus halving problem. While recent work has shown that the approximate version of this problem is PPA-complete [Filos-Ratsikas and Goldberg, 2018; Filos-Ratsikas and Goldberg, 2018], we show that the exact version is much harder. Specifically, finding a solution with n agents and n cuts is FIXP-hard, and deciding whether there exists a solution with fewer than n cuts is ETR-complete. We also give a QPTAS for the case where each agent’s valuation is a polynomial. Along the way, we define a new complexity class BU, which captures all problems that can be reduced to solving an instance of the Borsuk-Ulam problem exactly. We show that FIXP subseteq BU subseteq TFETR and that LinearBU = PPA, where LinearBU is the subclass of BU in which the Borsuk-Ulam instance is specified by a linear arithmetic circuit.
Cite as

Argyrios Deligkas, John Fearnley, Themistoklis Melissourgos, and Paul G. Spirakis. Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 138:1-138:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{deligkas_et_al:LIPIcs.ICALP.2019.138,
  author =	{Deligkas, Argyrios and Fearnley, John and Melissourgos, Themistoklis and Spirakis, Paul G.},
  title =	{{Computing Exact Solutions of Consensus Halving and the Borsuk-Ulam Theorem}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{138:1--138:14},
  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.2019.138},
  URN =		{urn:nbn:de:0030-drops-107141},
  doi =		{10.4230/LIPIcs.ICALP.2019.138},
  annote =	{Keywords: PPA, FIXP, ETR, consensus halving, circuit, reduction, complexity class}
}
  • Refine by Type
  • 4 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 2 2025
  • 1 2024
  • 1 2019

  • Refine by Author
  • 2 Melissourgos, Themistoklis
  • 1 Asadi, Ali
  • 1 Brice, Léonard
  • 1 Chatterjee, Krishnendu
  • 1 Coester, Christian
  • Show More...

  • Refine by Series/Journal
  • 4 LIPIcs

  • Refine by Classification
  • 1 Mathematics of computing → Combinatorial optimization
  • 1 Theory of computation → Algorithmic game theory
  • 1 Theory of computation → Automata over infinite objects
  • 1 Theory of computation → Complexity classes
  • 1 Theory of computation → Computational complexity and cryptography
  • Show More...

  • Refine by Keyword
  • 2 Smoothed Analysis
  • 1 Approximation
  • 1 Competitive Analysis
  • 1 ETR
  • 1 Existential Theory of Reals
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact