This paper introduces a general multiagent matroid upgrading problem that models a broad class of real-world resource allocation tasks. In this setting, there are multiple agents and a ground set of elements, where each element is assigned to a specific agent and has two associated costs: a default cost and a reduced (upgraded) cost. Upgrading an element lowers its cost to the upgraded value, while non-upgraded elements retain their default costs. Each agent is associated with its own matroid, with the goal of finding a minimum-cost basis. The central task is to select at most k elements to upgrade so as to minimize a non-decreasing convex function over the agents' minimum basis costs, capturing both efficiency and fairness objectives in multiagent systems.

翻译：本文提出了一种通用的多主体拟阵升级问题，该问题建模了广泛的实际资源分配任务。在该设定中，存在多个主体和一个基础元素集合，每个元素被分配给特定主体并具有两种关联成本：默认成本和降低（升级）成本。升级某个元素可将其成本降至升级后的值，而未升级的元素则保持其默认成本。每个主体关联其自身的拟阵，目标是为每个主体找到最小成本基。核心任务是选择最多k个元素进行升级，以最小化关于各主体最小基成本的非递减凸函数，从而在多主体系统中兼顾效率与公平性目标。