带私有采样的不确定联盟博弈中分配的概率近似正确稳定性
Probably approximately correct stability of allocations in uncertain coalitional games with private sampling
AI总结：
针对带私有采样的不确定联盟博弈中智能体对大联盟稳定性认知不同的问题，基于PAC学习框架提出研究核中分配样本外联盟合理性的新方法，给出先验后验保证、分布式压缩集算法及ζ-核的概率稳定性结论。
摘要：
我们研究联盟值存在外生不确定性的联盟博弈，其中每个智能体可拥有不确定性的私有样本。因此，智能体对大联盟稳定性的认知可能存在差异。在此背景下，我们提出一种新方法，研究稳定分配集（即核（core））中分配的样本外联盟合理性。我们的分析建立在概率近似正确（probably approximately correct，PAC）学习框架之上。首先，我们给出了整个核的先验与后验保证。此外，我们提供了一种分布式算法，用于计算决定后验结论泛化性质的压缩集。随后，我们将分析细化到单个收益分配，同样采用先验和后验两种方法，优化了我们的概率鲁棒性界。最后，我们考虑了松弛的ζ-核（ζ-core）以纳入邻近分配，同时也处理了核为空的情况。针对该情况，我们给出了ζ-核中分配最终稳定性的概率表述。
英文摘要：
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 $ζ$-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 $ζ$-core.
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