Computing Least Cores of Supermodular Cooperative Games
Authors: Daisuke Hatano, Yuichi Yoshida
AAAI 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we characterize the strong and the weak least cores of supermodular cooperative games using the theory of minimizing crossing submodular functions. We then apply our characterizations to two representative supermodular cooperative games, namely, the induced subgraph game generalized to hypergraphs and the airport game. For these games, we derive explicit forms of the strong and weak least core values, and provide polynomial-time algorithms that compute value divisions in the strong and weak least cores. |
| Researcher Affiliation | Collaboration | Daisuke Hatano National Institute of Informatics JST, ERATO, Kawarabayashi Large Graph Project hatano@nii.ac.jp Yuichi Yoshida National Institute of Informatics, and Preferred Infrastructure, Inc. yyoshida@nii.ac.jp |
| Pseudocode | Yes | Algorithm 1 Input: A hypergraph G = (V, E, w). Output: The strong least core value of G. |
| Open Source Code | No | The paper does not provide any concrete access to source code, such as a specific repository link or an explicit code release statement. |
| Open Datasets | No | The paper is theoretical, focusing on mathematical characterizations and algorithms for cooperative games. It does not involve empirical studies with datasets, training, or testing. Thus, there is no mention of publicly available or open datasets in the context of experiments. |
| Dataset Splits | No | The paper is theoretical, focusing on mathematical characterizations and algorithms for cooperative games. It does not involve empirical studies with dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper focuses on theoretical characterizations and algorithm design, not on empirical performance evaluation. Therefore, there is no mention of specific hardware used for running experiments. |
| Software Dependencies | No | The paper mentions mathematical concepts and algorithms (e.g., 'ellipsoid method', 'max flow min cut computation'), but it does not specify any concrete software, libraries, or solvers with version numbers that would be needed to replicate implementation details. |
| Experiment Setup | No | The paper describes algorithms and theoretical characterizations but does not detail an experimental setup, such as hyperparameter values or training configurations, as it does not conduct empirical experiments. |