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 [1].
Competitive Equilibria with a Constant Number of Chores
Authors: Jugal Garg, Peter McGlaughlin, Martin Hoefer, Marco Schmalhofer
JAIR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study markets with mixed manna, where m divisible goods and chores shall be divided among n agents to obtain a competitive equilibrium. Equilibrium allocations are known to satisfy many fairness and efficiency conditions. While a lot of recent work in fair division is restricted to linear utilities and chores, we focus on a substantial generalization to separable piecewise-linear and concave (SPLC) utilities and mixed manna. We first derive polynomial-time algorithms for markets with a constant number of items or a constant number of agents. Our main result is a polynomial-time algorithm for instances with a constant number of chores (as well as any number of goods and agents) under the condition that chores dominate the utility of the agents. |
| Researcher Affiliation | Academia | Jugal Garg EMAIL Peter Mc Glaughlin EMAIL University of Illinois, Urbana-Champaign, IL, USA Martin Hoefer EMAIL Marco Schmalhofer EMAIL Goethe University, Frankfurt am Main, Hessen, Germany |
| Pseudocode | Yes | Algorithm 1: Forced and flexible segments F and ˆF of agent i in a sub-cell |
| Open Source Code | No | The paper focuses on theoretical algorithms and their complexity analysis. There is no mention of open-source code, a code repository, or supplementary materials containing code for the described methodology. |
| Open Datasets | No | We study markets with mixed manna, where m divisible goods and chores shall be divided among n agents to obtain a competitive equilibrium. The paper defines a theoretical model and discusses algorithms for it, but does not use any specific datasets for experimental evaluation. |
| Dataset Splits | No | This paper is theoretical in nature, focusing on algorithms and complexity analysis for competitive equilibria. It does not involve empirical experiments with datasets, and therefore no dataset split information is provided. |
| Hardware Specification | No | This paper is theoretical, presenting algorithms and complexity analysis. It does not describe any empirical experiments, and therefore no specific hardware details are provided. |
| Software Dependencies | No | This paper focuses on theoretical algorithms and their complexity. There is no mention of specific software, libraries, or solvers with version numbers that would be used for empirical experiments. |
| Experiment Setup | No | This paper is theoretical in nature, proposing algorithms and analyzing their complexity rather than conducting empirical experiments. Therefore, no experimental setup details, hyperparameters, or training configurations are provided. |