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On axiomatizations of the Shapley value for assignment games

Brink, van den René and Pintér, Miklós (2012) On axiomatizations of the Shapley value for assignment games. Discussion Paper. Tinbergen Institute.

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Abstract

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 have 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.

Item Type:Monograph (Discussion Paper)
Series Name:Tinbergen Institute Discussion Paper
Series Number / Identification Number:TI 2012-092/II
Uncontrolled Keywords:assignment game, Shapley value, communication graph game, submarket e�ciency, valuation fairness, JEL: C71, C78
Subjects:Mathematics, Econometrics
Funders:J�anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, OTKA
ID Code:911
Deposited By: Ádám Hoffmann
Deposited On:25 Sep 2012 14:37
Last Modified:25 Sep 2012 14:37

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