Random partitions, potential, value, and externalities

• 成果类型: Article
• 署名作者: Casajus, Andre; Funaki, Yukihiko; Huettner, Frank
• 署名单位: HHL Leipzig Graduate School of Management; Waseda University; Sungkyunkwan University (SKKU)
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2024.06.004
• 发表日期: 2024
• 页码: 88-106
• 关键词: Shapley value; Partition function form; Random partition; Restriction operator; Ewens distribution; Chinese restaurant process; potential; externalities; null player; Expected accumulated worth

摘要

The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This computation integrates the coalition formation of all players and readily extends to games with externalities. We investigate those potential functions for games with externalities that can be computed this way. It turns out that the potential that corresponds to the MPW solution introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339-356) is unique in the following sense. It is obtained as the expected accumulated worth of a random partition, it generalizes the potential for games without externalities, and it induces a solution that satisfies the null player property even in the presence of externalities.