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Induced Representations in Cooperative Games with Homogeneous Groups of Players

  • Windsor Kiang
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Abstract

Oftentimes, the Shapley value, a measure of the contribution of a player to a game, becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of a homogeneous group game by using an induced representation from a Young subgroup. We prove that the depth of interaction of a two-group game is limited by the size of the minority group. Therefore, the algebraic structure of the game filters out a large space of irrelevant complexities. We then show that this filtration constrains any symmetric linear value to a specific subspace. This recovers the Shapley value uniquely for games consisting of exactly two homogeneous groups under standard axioms. Finally, we explore applications to the UN Security Council and complementary goods markets to illustrate the practical power of this approach.

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Cite

BibTeXRIS
BibTeX
@misc{kiang2026induced,
  title = {{Induced Representations in Cooperative Games with Homogeneous Groups of Players}},
  author = {Windsor Kiang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.00962},
  eprint = {2605.00962},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.00962},
}
RIS
TY  - UNPB
TI  - Induced Representations in Cooperative Games with Homogeneous Groups of Players
AU  - Windsor Kiang
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.00962
UR  - https://arxiv.org/abs/2605.00962
AB  - Oftentimes, the Shapley value, a measure of the contribution of a player to a game, becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of a homogeneous group game by using an induced representation from a Young subgroup. We prove that the depth of interaction of a two-group game is limited by the size of the minority group. Therefore, the algebraic structure of the game filters out a large space of irrelevant complexities. We then show that this filtration constrains any symmetric linear value to a specific subspace. This recovers the Shapley value uniquely for games consisting of exactly two homogeneous groups under standard axioms. Finally, we explore applications to the UN Security Council and complementary goods markets to illustrate the practical power of this approach.
ER  -