拟阵打包博弈：核心与核仁
Matroid Packing Games: The Core and the Nucleolus
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中文总结 AI 辅助
本文定义拟阵基打包博弈，推广网络强度博弈，利用拟阵交换结构构建图论框架，实现核心非空性测试、核心分配及核仁计算的多项式时间算法。
中文摘要 AI 辅助
本文从合作博弈论的视角研究拟阵基打包问题，并定义了相应的拟阵基打包博弈。该模型将Baiou和Barahona（2020）的网络强度博弈从图拟阵推广到一般拟阵。基于拟阵的交换结构，我们发展了一个图论框架来分析该博弈的核心与核仁。该框架给出了核心非空性的紧凑刻画，并使得测试核心非空性、寻找核心分配以及计算核仁的多项式时间算法成为可能。特别地，该方法为Baiou和Barahona（2020）研究的网络强度博弈中出现的核仁计算问题提供了一个更广泛且更具结构性的框架，涵盖了核心非空和核心为空两种情况。
英文摘要
In this paper, we study the matroid base packing problem from the perspective of cooperative game theory and define the associated matroid base packing game. This model extends the network strength game of Baiou and Barahona (2020) from graphic matroids to general matroids. Building on the exchange structure of matroid, we develop a graph theoretic framework for analyzing the core and the nucleolus in this game. This framework yields a compact characterization of core nonemptiness and enables polynomial time algorithms for testing core nonemptiness, finding a core allocation, and computing the nucleolus. In particular, the approach provides a broader and more structured framework for the nucleolus computation problem arising in network strength games studied by Baiou and Barahona (2020), covering both the nonempty core and empty core cases.
发表机构
- School of Mathematical Sciences, Ocean University of China（中国海洋大学数学科学学院）
- Faculty of Information Science and Engineering, Ocean University of China（中国海洋大学信息科学与工程学院）
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