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Random partitions, potential, value, and externalities

Author

Listed:
  • Casajus, André
  • Funaki, Yukihiko
  • Huettner, Frank

Abstract

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.

Suggested Citation

  • Casajus, André & Funaki, Yukihiko & Huettner, Frank, 2024. "Random partitions, potential, value, and externalities," Games and Economic Behavior, Elsevier, vol. 147(C), pages 88-106.
    • Handle: RePEc:eee:gamebe:v:147:y:2024:i:c:p:88-106
    DOI: 10.1016/j.geb.2024.06.004
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    Keywords

    Shapley value; Partition function form; Random partition; Restriction operator; Ewens distribution; Chinese restaurant process; Potential; Externalities; Null player; Expected accumulated worth;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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