Corpus ID: 236171392

Hodge theoretic reward allocation for generalized cooperative games on graphs

@article{Lim2021HodgeTR,
  title={Hodge theoretic reward allocation for generalized cooperative games on graphs},
  author={Tongseok Lim},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.10510}
}
  • Tongseok Lim
  • Published 2021
  • Mathematics, Computer Science, Economics
  • ArXiv
We define cooperative games on general graphs and generalize Lloyd S. Shapley’s celebrated allocation formula for those games in terms of stochastic path integral driven by the associated Markov chain on each graph. We then show that the value allocation operator, one for each player defined by the stochastic path integral, coincides with the player’s component game which is the solution to the least squares (or Poisson’s) equation, in light of the combinatorial Hodge decomposition on general… Expand
1 Citations
A Hodge Theoretic Extension of Shapley Axioms
  • Tongseok Lim
  • Mathematics, Computer Science
  • SSRN Electronic Journal
  • 2021
TLDR
A new set of axioms is proposed which characterizes the component games given by Stern and Tettenhorst, thereby suggesting that the component values for every coalition state may also serve for a valid measure of fair allocation among the players in each coalition. Expand

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A Hodge Theoretic Extension of Shapley Axioms
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  • Mathematics, Computer Science
  • SSRN Electronic Journal
  • 2021
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A new set of axioms is proposed which characterizes the component games given by Stern and Tettenhorst, thereby suggesting that the component values for every coalition state may also serve for a valid measure of fair allocation among the players in each coalition. Expand
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