Decomposition of solutions and the Shapley value

• 成果类型: Article
• 署名作者: Casajus, Andre; Huettner, Frank
• 署名单位: HHL Leipzig Graduate School of Management; European School of Management & Technology
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.05.001
• 发表日期: 2018
• 页码: 37-48
• 关键词: decomposition; Shapley value; potential; Consistency; Higher-order contributions; Balanced contributions

摘要

We suggest foundations for the Shapley value and for the naive solution, which assigns to any player the difference between the worth of the grand coalition and its worth after this player left the game. To this end, we introduce the decomposition of solutions for cooperative games with transferable utility. A decomposer of a solution is another solution that splits the former into a direct part and an indirect part. While the direct part (the decomposer) measures a player's contribution in a game as such, the indirect part indicates how she affects the other players' direct contributions by leaving the game. The Shapley value turns out to be unique decomposable decomposer of the naive solution. (C) 2017 Elsevier Inc. All rights reserved.