Game Representations and Extensions of the Shapley Value
arxiv(2024)
摘要
We show that any cooperative game can be represented by an assignment of
costly facilities to players, in which it is intuitively obvious how to
allocate the total cost in an equitable manner. This equitable solution turns
out to be the Shapley value of the game, and thus provides as an alternative
justification of the value. Game representations also open the door for
extending the Shapley value to situations where not all coalitions can form,
provided those that can constitute a "semi-algebra"; or, more generally, a
"hierarchy"; or, still more generally, have "full span".
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