Computing Near-Optimal Stable Cost Allocations for Cooperative Games by Lagrangian Relaxation
针对核心为空集的成本分摊合作博弈，提出基于拉格朗日松弛的框架来计算近似最优且满足联盟稳定约束的成本分配，相比线性规划方法能获得更优解或替代最优解。
For a cost-sharing cooperative game with an empty core, we study the problem of calculating a near-optimal cost allocation that satisfies coalitional stability constraints and maximizes the total cost allocated to all players. One application of such a problem is finding the minimum level of subsidy required to stabilize the grand coalition. To obtain solutions, we propose a new generic framework based on Lagrangian relaxation, which has several advantages over existing work that exclusively relies on linear programming (LP) relaxation techniques. Our approach can generate better cost allocations than LP-based algorithms, and is also applicable to a broader range of problems. To illustrate the efficiency and performance of the Lagrangian relaxation framework, we investigate two different facility location games. The results demonstrate that our new approach can find better cost allocations than the LP-based algorithm, or provide alternative optimal cost allocations for cases that the LP-based algorithm can also solve to optimality.