联盟形成中估值更新下的稳定性
Stability Under Valuation Updates in Coalition Formation
AI总结：
本文研究了在代理人估值变化下联盟形成中的稳定性问题，证明了多种稳定性概念下的NP完全性，并提出了在受限对称估值下的多项式时间算法以保证长期更新中的稳定性。
摘要：
联盟形成研究如何在考虑代理人偏好的情况下将一组代理人划分为不相交的联盟。我们研究了在一种加性可分离的享乐博弈变体中稳定性经典目标，其中代理人可以改变他们的估值。我们的目标是在每次变化后找到稳定的划分。为了最小化重新配置成本，我们寻找附近的稳定联盟结构。我们的重点是基于单个代理人偏离的稳定性概念。我们详细描绘了在加性可分离的享乐博弈中寻找附近稳定联盟结构的复杂性，针对对称和非对称估值。我们的结果表明，对于纳什稳定性、个人稳定性、合同纳什稳定性和合同个人稳定性，该问题都是NP完全的。我们通过在受限对称估值下为合同纳什稳定性和合同个人稳定性提供多项式时间算法来补充这些结果。最后，我们证明这些算法在长期更新序列中能保证平均距离有界。
英文摘要：
Coalition formation studies how to partition a set of agents into disjoint coalitions under consideration of their preferences. We study the classical objective of stability in a variant of additively separable hedonic games where agents can change their valuations. Our objective is to find a stable partition after each change. To minimize the reconfiguration cost, we search for nearby stable coalition structures. Our focus is on stability concepts based on single-agent deviations. We present a detailed picture of the complexity of finding nearby stable coalition structures in additively separable hedonic games, for both symmetric and non-symmetric valuations. Our results show that the problem is NP-complete for Nash stability, individual stability, contractual Nash stability, and contractual individual stability. We complement these results by presenting polynomial-time algorithms for contractual Nash stability and contractual individual stability under restricted symmetric valuations. Finally, we show that these algorithms guarantee a bounded average distance over long sequences of updates.
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