Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Approximate Nash Equilibria with Near Optimal Social Welfare
Authors: Artur Czumaj, Michail Fasoulakis, Marcin Jurdzinski
IJCAI 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we show that for every fixed ε > 0, every bimatrix game (with values in [0, 1]) has an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor, (1 1 ε)2, of the optimum. Furthermore, our result can be made algorithmic in the following sense: for every fixed 0 ε < ε, if we can find an ε -approximate Nash equilibrium in polynomial time, then we can find in polynomial time an ε-approximate Nash equilibrium with the total payoff of the players at least a constant factor of the optimum. Our analysis is especially tight in the case when ε 1 2. In this case, we show that for any bimatrix game there is an ε-approximate Nash equilibrium with constant size support whose social welfare is at least 2 ε ε 0.914 times the optimal social welfare. Furthermore, we demonstrate that our bound for the social welfare is tight, that is, for every ε 1 2 there is a bimatrix game for which every ε-approximate Nash equilibrium has social welfare at most 2 ε ε times the optimal social welfare. |
| Researcher Affiliation | Academia | Department of Computer Science Centre for Discrete Mathematics and its Applications (DIMAP) University of Warwick, United Kingdom |
| Pseudocode | Yes | ε-APPROXIMATE NASH (R, C, ε) Find i, j such that Rij + Cij is maximized. Find r, c such that Rrj is maximized and Cic is maximized. If Rrj Rij ε and Cic Cij ε, then return strategy profile (i, j). If Rrj Rij < ε and Cic Cij > ε, then set p = ε Cic Cij and return strategy profile (i, pj + (1 p)c). If Rrj Rij > ε and Cic Cij < ε, then set p = ε Rrj Rij and return strategy profile (pi + (1 p)r, j). |
| Open Source Code | No | The paper does not contain any statements about releasing source code or links to a code repository. |
| Open Datasets | No | This is a theoretical paper and does not describe empirical experiments with datasets. Thus, there is no mention of dataset availability for training. |
| Dataset Splits | No | This is a theoretical paper and does not describe empirical experiments with datasets, and therefore no dataset split information for validation is provided. |
| Hardware Specification | No | This is a theoretical paper that focuses on algorithm design and proofs, not empirical experiments. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | This is a theoretical paper focused on mathematical proofs and algorithms, not practical implementation or empirical experiments. Therefore, no software dependencies with version numbers are mentioned. |
| Experiment Setup | No | This is a theoretical paper and does not describe empirical experiments, thus no experimental setup details like hyperparameters or training settings are provided. |