Arbeitspapier
On Axiomatizations of the Shapley Value for Assignment Games
We consider the problem of axiomatizing the Shapley value on the class of assignment games. We first show that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games by providing alternative solutions that satisfy these axioms. However, when considering an assignment game as a communication graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph buyers are connected with sellers only, we show that Myerson's component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set hav e zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.
- Language
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Englisch
- Bibliographic citation
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Series: Tinbergen Institute Discussion Paper ; No. 12-092/II
- Classification
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Wirtschaft
Cooperative Games
Bargaining Theory; Matching Theory
- Subject
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Assignment game
Shapley value
communication graph game
submarket efficiency
valuation fairness
Shapley-Wert
Kooperatives Spiel
Transferable Utility Games
Theorie
- Event
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Geistige Schöpfung
- (who)
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van den Brink, Rene
Pinter, Miklos
- Event
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Veröffentlichung
- (who)
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Tinbergen Institute
- (where)
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Amsterdam and Rotterdam
- (when)
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2012
- Handle
- Last update
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10.03.2025, 11:43 AM CET
Data provider
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Object type
- Arbeitspapier
Associated
- van den Brink, Rene
- Pinter, Miklos
- Tinbergen Institute
Time of origin
- 2012
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Axiomatization and Implementation of Discounted Shapley Values
Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems
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A Note on the Shapley Value for Characteristic Functions on Bipartitions
Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution
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Axiomatization and Implementation of Discounted Shapley Values
Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems
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