2 Search Results for "Frederiksen, Søren Kristoffer Stiil"

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)

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@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.MFCS.2018.24
Hardness Results for Consensus-Halving

Authors: Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, and Jie Zhang

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
The Consensus-halving problem is the problem of dividing an object into two portions, such that each of n agents has equal valuation for the two portions. We study the epsilon-approximate version, which allows each agent to have an epsilon discrepancy on the values of the portions. It was recently proven in [Filos-Ratsikas and Goldberg, 2018] that the problem of computing an epsilon-approximate Consensus-halving solution (for n agents and n cuts) is PPA-complete when epsilon is inverse-exponential. In this paper, we prove that when epsilon is constant, the problem is PPAD-hard and the problem remains PPAD-hard when we allow a constant number of additional cuts. Additionally, we prove that deciding whether a solution with n-1 cuts exists for the problem is NP-hard.
Cite as

Aris Filos-Ratsikas, Søren Kristoffer Stiil Frederiksen, Paul W. Goldberg, and Jie Zhang. Hardness Results for Consensus-Halving. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{filosratsikas_et_al:LIPIcs.MFCS.2018.24,
  author =	{Filos-Ratsikas, Aris and Frederiksen, S{\o}ren Kristoffer Stiil and Goldberg, Paul W. and Zhang, Jie},
  title =	{{Hardness Results for Consensus-Halving}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{24:1--24:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.24},
  URN =		{urn:nbn:de:0030-drops-96069},
  doi =		{10.4230/LIPIcs.MFCS.2018.24},
  annote =	{Keywords: PPAD, PPA, consensus halving, generalized-circuit, reduction}
}
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