Probably approximately correct stability of allocations in uncertain coalitional games with private sampling
We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology t...
| Main Authors: | , , , , |
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| Format: | Conference item |
| Language: | English |
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Journal of Machine Learning Research
2024
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| _version_ | 1826313671839580160 |
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| author | Pantazis, G Fele, F Fabiani, F Grammatico, S Margellos, K |
| author_facet | Pantazis, G Fele, F Fabiani, F Grammatico, S Margellos, K |
| author_sort | Pantazis, G |
| collection | OXFORD |
| description | We study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed zeta-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the zeta-core. |
| first_indexed | 2024-04-09T03:57:41Z |
| format | Conference item |
| id | oxford-uuid:4ac47a91-4c60-4f42-a8e2-175a36f2b763 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:18:42Z |
| publishDate | 2024 |
| publisher | Journal of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:4ac47a91-4c60-4f42-a8e2-175a36f2b7632024-07-29T10:25:28ZProbably approximately correct stability of allocations in uncertain coalitional games with private samplingConference itemhttp://purl.org/coar/resource_type/c_5794uuid:4ac47a91-4c60-4f42-a8e2-175a36f2b763EnglishSymplectic ElementsJournal of Machine Learning Research2024Pantazis, GFele, FFabiani, FGrammatico, SMargellos, KWe study coalitional games with exogenous uncertainty in the coalition value, in which each agent is allowed to have private samples of the uncertainty. As a consequence, the agents may have a different perception of stability of the grand coalition. In this context, we propose a novel methodology to study the out-of-sample coalitional rationality of allocations in the set of stable allocations (i.e., the core). Our analysis builds on the framework of probably approximately correct learning. Initially, we state a priori and a posteriori guarantees for the entire core. Furthermore, we provide a distributed algorithm to compute a compression set that determines the generalization properties of the a posteriori statements. We then refine our probabilistic robustness bounds by specialising the analysis to a single payoff allocation, taking, also in this case, both a priori and a posteriori approaches. Finally, we consider a relaxed zeta-core to include nearby allocations and also address the case of empty core. For this case, probabilistic statements are given on the eventual stability of allocations in the zeta-core. |
| spellingShingle | Pantazis, G Fele, F Fabiani, F Grammatico, S Margellos, K Probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
| title | Probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
| title_full | Probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
| title_fullStr | Probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
| title_full_unstemmed | Probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
| title_short | Probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
| title_sort | probably approximately correct stability of allocations in uncertain coalitional games with private sampling |
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