AI 中文总结
本研究证明固定服务器数量下计数负载分配博弈的无政府状态价格为$\Theta_M(\kappa^{1-2^{-M}})$，通过公共乘数证书等方法给出上界，并构造匹配链族证明紧致性，同时用合成实验验证理论结果。
AI 中文摘要
边际贡献定价使社会目标成为精确势函数，但并不保证每个稳定分配都是高效的。我们研究具有异构工作负载的不可分割客户端、任意非负分配成本以及客户端在固定数量共享服务器和可选本地执行上的私有资格菜单。每个服务器的社会成本是其占用率乘以其总工作负载和服务器特定系数。对于每个固定服务器上限$M$，我们证明当工作负载比率上限$\kappa$增长时，该类博弈的无政府状态价格为$\Theta_M(\kappa^{1-2^{-M}})$。上界适用于每个均衡和每个可行比较，无需无环比较或强连通分量限制。其证明结合了公共乘数证书、源加权残差不等式和有序矩递推。一个匹配的链族可通过移动无人机（UAV）客户端和固定地面服务器实现，具有正高度、正宽度覆盖和明确支付的无线基线。我们证明了精确航点消除并给出了输入可计算的组件细化。调度和拥塞恒等式界定了哪些已有界可转移。对2,800个合成博弈的精确枚举识别出低效均衡，而270个主参数化合成实例预算记录评估了相对于可行多起点参考的增量延迟。紧致性涉及固定$M$的异质性指数，而非匹配领先常数或最坏情况配置的实测频率。
英文摘要
Marginal-contribution pricing makes the social objective an exact potential, but does not ensure that every stable assignment is efficient. We study indivisible clients with heterogeneous workloads, arbitrary nonnegative assignment costs, and private eligibility menus over a fixed number of shared servers and optional local execution. Each server's social cost is its occupancy multiplied by its aggregate workload and a server-specific coefficient. For every fixed server cap $M$, we prove that the price of anarchy over this class is $Θ_M(κ^{1-2^{-M}})$ as the workload-ratio cap $κ$ grows. The upper bound applies to every equilibrium and every feasible comparison, without an acyclic-comparison or strongly-connected-component restriction. Its proof combines a common-multiplier certificate, a source-weighted residual inequality and an ordered moment recurrence. A matching chain family has a realization by mobile unmanned aerial vehicle (UAV) clients and fixed ground servers, with positive altitude, positive-width coverage and an explicitly paid wireless baseline. We prove exact waypoint elimination and give an input-computable component refinement. Scheduling and congestion identities delimit which established bounds transfer. Exact enumeration of 2,800 synthetic games identifies inefficient equilibria, while 270 primary-parameterized synthetic instance-budget records evaluate incremental latency relative to a feasible multistart reference. Tightness concerns the heterogeneity exponent for fixed $M$, not matching leading constants or measured frequency of the worst-case configurations.
CommentsThe manuscript is incomplete and requires substantial additional work before it is ready for dissemination
