Simultaneous Penalization and Subsidization for Stabilizing Grand Cooperation

• 成果类型: Article
• 署名作者: Liu, Lindong; Qi, Xiangtong; Xu, Zhou
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; Hong Kong University of Science & Technology; Hong Kong Polytechnic University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2018.1723
• 发表日期: 2018
• 页码: 1362-1375
• 关键词: Cost allocation; least core; games

摘要

In this paper we propose a new instrument, a simultaneous penalization and subsidization, for stabilizing the grand coalition and enabling cooperation among all players of an unbalanced cooperative game. The basic idea is to charge a penalty z from players who leave the grand coalition, and at the same time provide a subsidy omega to players who stay in the grand coalition. To formalize this idea, we establish a penalty-subsidy function omega(z) based on a linear programming model, which allows a decision maker to quantify the trade-off between the levels of penalty and subsidy. By studying function omega(z), we identify certain properties of the trade-off. To implement the new instrument, we design two algorithms to construct function omega(z) and its approximation. Both algorithms rely on solving the value of omega(z) for any given z, for which we propose two effective solution approaches. We apply the new instrument to a class of machine scheduling games, showing its wide applicability.