On axiomatizations of the Shapley value for assignment games

Rene van den Brink () and Miklós Pintér

Journal of Mathematical Economics, 2015, vol. 60, issue C, 110-114

Abstract: We consider the problem of axiomatizing the Shapley value on the class of assignment games. It turns out 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. 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 where buyers (sellers) are connected with sellers (buyers) 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.

Keywords: Game theory; Assignment game; Shapley value; Graph game; Submarket efficiency; Valuation fairness (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

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Working Paper: On Axiomatizations of the Shapley Value for Assignment Games (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:60:y:2015:i:c:p:110-114

DOI: 10.1016/j.jmateco.2015.06.016

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