Probably approximately correct stability of allocations in uncertain coalitional games with private sampling
CoRR(2023)
摘要
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.
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