Axiomatic and Probabilistic Foundations for the Hodge-Theoretic Shapley Value
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866914087033634816 |
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| author | Lim, Tongseok |
| author_facet | Lim, Tongseok |
| contents | This paper establishes a complete theoretical foundation for the Hodge-theoretic extension of the Shapley value introduced by Stern and Tettenhorst (2019). We show that a set of five axioms--efficiency, linearity, symmetry, a modified null-player condition, and an independency principle--uniquely characterize this value across all coalitions, not just the grand coalition. In parallel, we derive a probabilistic representation interpreting each player's value as the expected cumulative marginal contribution along a random walk on the coalition graph. These dual axiomatic and probabilistic results unify fairness and stochastic interpretation, positioning the Hodge-theoretic value as a canonical generalization of Shapley's framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_15094 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Axiomatic and Probabilistic Foundations for the Hodge-Theoretic Shapley Value Lim, Tongseok Optimization and Control Computer Science and Game Theory Theoretical Economics 91A12, 05C57, 60J20, 68R01 This paper establishes a complete theoretical foundation for the Hodge-theoretic extension of the Shapley value introduced by Stern and Tettenhorst (2019). We show that a set of five axioms--efficiency, linearity, symmetry, a modified null-player condition, and an independency principle--uniquely characterize this value across all coalitions, not just the grand coalition. In parallel, we derive a probabilistic representation interpreting each player's value as the expected cumulative marginal contribution along a random walk on the coalition graph. These dual axiomatic and probabilistic results unify fairness and stochastic interpretation, positioning the Hodge-theoretic value as a canonical generalization of Shapley's framework. |
| title | Axiomatic and Probabilistic Foundations for the Hodge-Theoretic Shapley Value |
| topic | Optimization and Control Computer Science and Game Theory Theoretical Economics 91A12, 05C57, 60J20, 68R01 |
| url | https://arxiv.org/abs/2106.15094 |