AI 中文总结
研究网络分配博弈中代理匿名且具策略性，基于代理效用函数和拓扑，给出多种稳定性概念下稳定分配存在性与难解性二分法，还证明计算福利最大化分配及验证帕累托最优的强难解性。
AI 中文摘要
我们研究网络分配博弈，其中一组代理必须被分配到图拓扑的（一个子集的）顶点上。代理是匿名且具有策略性的：每个代理旨在最大化其效用，该效用是其分配顶点邻域中代理数量的函数。我们专注于各种稳定性概念下稳定分配的存在性和计算。具体而言，我们研究基于交换的稳定性概念（代理可相互交换位置）和基于跳跃的稳定性概念（代理可跳到图中的空顶点）。对于几乎所有我们考虑的稳定性概念，我们根据代理效用函数的结构和拓扑给出存在性与难解性之间的二分法。此外，我们证明了计算福利最大化分配以及验证给定分配是否为帕累托最优的强难解性结果。
英文摘要
We study network allocation games in which a set of agents must be allocated to (a subset of) the vertices of a graph topology. The agents are anonymous and strategic: Each of them aims to maximize her utility, which is a function of the number of agents in the neighborhood of their allocated vertex. We focus on the existence and the computation of stable allocations under various notions of stability. More specifically, we study swap-based stability notions, where agents can exchange locations between them, and jump-based stability notions, where agents can jump to an empty vertex of the graph. For almost all stability notions we consider, we provide dichotomies between existence and intractability that depend on the structure of the utility functions of the agents and the topology. In addition, we prove strong intractability results for computing welfare-maximizing allocations and for verifying whether a given allocation is Pareto optimal.
CommentsA preliminary version appeared in SAGT '26
