This paper addresses the optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. This means that all subsets of agents have an outside option at a certain cost, and stability requires that the cost shares are defined so that none of the outside options is preferable. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The paper gives a fairly complete picture of the computational complexity of this optimization problem, in relation to classical computational problems on the core. We also show that, for games with an empty core, the problem is equivalent to computing minimal core relaxations for several relaxations that have been proposed earlier. As an example for a class of cost sharing games with non-empty core, we address minimum cost spanning tree games. While it is known that cost shares in the core can be found efficiently, we show that the computation of maximal cost shares is NP-hard for minimum cost spanning tree games. We also derive a 2-approximation algorithm. Our work opens several directions for future work.

翻译：本文研究了在满足合作可转移效用博弈（TU博弈）核心约束的稳定性条件下，最大化一组智能体之间可分摊总成本的优化问题。这意味着所有智能体子集都具有以特定成本获得的外部选择，而稳定性要求成本分摊的定义应使任何外部选择均不具备优势。当最大化可分摊总成本时，成本分摊必须满足定义TU博弈核心的所有约束条件，但预算平衡约束除外。本文全面刻画了该优化问题与核心经典计算问题之间的计算复杂性关系。我们还证明，对于核心为空的对策，该问题等价于计算几种先前提出的核心松弛的最小松弛。以具有非空核心的成本分摊对策类为例，我们研究了最小成本生成树对策。尽管已知可高效找到核心中的成本分摊，但我们证明对于最小成本生成树对策，最大成本分摊的计算是NP难的，并据此推导出一个2-近似算法。我们的工作为未来研究开辟了若干方向。