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].
Arbitration and Stability in Cooperative Games with Overlapping Coalitions
Authors: Y. Zick, E. Markakis, E. Elkind
JAIR 2014 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our main contribution is a broad generalization of the overlapping coalition formation (OCF) model proposed by Chalkiadakis et al. (2010). While Chalkiadakis et al. describe three ways in which nondeviators may react to a deviation, we propose a general framework for modeling such reactions. Our framework is based on the notion of arbitration function (Section 3). This is a function that, given a deviating group of players and its deviation, outputs, for every coalition containing the deviators, the amount that the deviators can expect to receive from this coalition post-deviation. Using arbitration functions, we present a class of solution concepts for OCF games that we call arbitrated cores (Section 4). We show that the three concepts of the core described by Chalkiadakis et al. (2010) are special cases of our model, and propose a new concept of the core, which we call the sensitive core. We provide a criterion for checking whether an outcome is in the arbitrated core, and characterize core outcomes under some important arbitration functions. We then focus on identifying sufficient and necessary conditions for the arbitrated core to be non-empty (Section 5). Building on the work of Chalkiadakis et al., who provide an LP-based criterion for the non-emptiness of the conservative core, we derive criteria for the sensitive and refined core to be non-empty. We use this result to identify an interesting class of OCF games whose refined core is guaranteed to be non-empty. Finally, we show that OCF games with the conservative arbitration function are essentially equivalent to non-OCF games, by relating the conservative core of an OCF game G to the core of its discrete superadditive cover, which is a non-OCF game that is constructed from G in a natural way. In particular, this means that the conservative core of an OCF game G is non-empty when the discrete superadditive cover of G is supermodular. We demonstrate that this condition is strictly weaker than the convexity-based condition for conservative core non-emptiness given by Chalkiadakis et al. |
| Researcher Affiliation | Academia | Yair Zick EMAIL School of Computer Science Carnegie Mellon University, United States Evangelos Markakis EMAIL Department of Informatics Athens University of Economics and Business, Greece Edith Elkind EMAIL Department of Computer Science University of Oxford, United Kingdom |
| Pseudocode | No | The paper uses mathematical definitions, theorems, and proofs to describe its framework and results. While it describes procedures and concepts, it does not include any explicitly labeled 'Pseudocode' or 'Algorithm' blocks, nor does it present structured steps in a code-like format. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or provide links to a code repository for the methodology described. |
| Open Datasets | No | The paper is theoretical in nature, focusing on game theory and arbitration functions. It does not conduct empirical experiments using datasets, and therefore, no information about publicly available or open datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experimentation with datasets. Therefore, it does not provide any information regarding training/test/validation dataset splits. |
| Hardware Specification | No | The paper focuses on theoretical concepts in cooperative game theory and does not describe any experimental setup that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and presents mathematical models and proofs. It does not mention any specific software dependencies with version numbers that would be required to reproduce experiments. |
| Experiment Setup | No | The paper is theoretical, presenting mathematical models and proofs for cooperative games. It does not describe any empirical experiments, and therefore, no experimental setup details, hyperparameters, or system-level training settings are provided. |