Random partitions, potential, value, and externalities
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914878648745984 |
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| author | Casajus, André Funaki, Yukihiko Huettner, Frank |
| author_facet | Casajus, André Funaki, Yukihiko Huettner, Frank |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random partitions, potential, value, and externalities Casajus, André Funaki, Yukihiko Huettner, Frank Theoretical Economics Computer Science and Game Theory Combinatorics 91A12 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. |
| title | Random partitions, potential, value, and externalities |
| topic | Theoretical Economics Computer Science and Game Theory Combinatorics 91A12 |
| url | https://arxiv.org/abs/2402.00394 |