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.

翻译：沙普利值等于一个参与者对博弈势函数的贡献。势函数是对博弈最自然的单值概括，可通过参与者随机划分的期望累积价值计算得出。这一计算方法整合了所有参与者的联盟形成过程，并能自然地推广至具有外部性的博弈。我们研究了那些可通过此方式计算的具有外部性的博弈势函数。结果表明，对应于Macho-Stadler等人（2007，《经济理论杂志》第135卷，339-356页）提出的MPW解法的势函数在以下意义上是唯一的：它通过随机划分的期望累积价值获得，推广了无外部性博弈的势函数，并且即使在存在外部性的情况下，其诱导的解仍满足零参与者性质。