On Axiomatizations of the Shapley Value for Assignment Games

Rene van den Brink () and Miklos Pinter
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Miklos Pinter: Corvinus University

No 12-092/II, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper led to a publication in the 'Journal of Mathematical Economics' , 2015, 60, 110-114.

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.

Keywords: Assignment game; Shapley value; communication graph game; submarket efficiency; valuation fairness (search for similar items in EconPapers)
JEL-codes: C71 C78 (search for similar items in EconPapers)
Date: 2012-09-13
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Journal Article: On axiomatizations of the Shapley value for assignment games (2015)
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