Probably approximately correct stability of allocations in uncertain coalitional games with private sampling

George Pantazis, Filiberto Fele, Filippo Fabiani, Sergio Grammatico, Kostas Margellos
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:1702-1714, 2024.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-pantazis24a, title = {Probably approximately correct stability of allocations in uncertain coalitional games with private sampling}, author = {Pantazis, George and Fele, Filiberto and Fabiani, Filippo and Grammatico, Sergio and Margellos, Kostas}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {1702--1714}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/pantazis24a/pantazis24a.pdf}, url = {https://proceedings.mlr.press/v242/pantazis24a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Probably approximately correct stability of allocations in uncertain coalitional games with private sampling %A George Pantazis %A Filiberto Fele %A Filippo Fabiani %A Sergio Grammatico %A Kostas Margellos %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-pantazis24a %I PMLR %P 1702--1714 %U https://proceedings.mlr.press/v242/pantazis24a.html %V 242 %X 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.
APA
Pantazis, G., Fele, F., Fabiani, F., Grammatico, S. & Margellos, K.. (2024). Probably approximately correct stability of allocations in uncertain coalitional games with private sampling. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:1702-1714 Available from https://proceedings.mlr.press/v242/pantazis24a.html.

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