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On Axiomatizations of the Shapley Value for Assignment Games

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Author Info

  • Rene van den Brink

    (VU University Amsterdam)

  • Miklos Pinter

    (Corvinus University)

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 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-092/II.

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Date of creation: 13 Sep 2012
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Handle: RePEc:dgr:uvatin:20120092

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Web page: http://www.tinbergen.nl

Related research

Keywords: Assignment game; Shapley value; communication graph game; submarket efficiency; valuation fairness;

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  1. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer, Springer, vol. 20(2), pages 183-90.
  2. Neyman, Abraham, 1989. "Uniqueness of the Shapley value," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(1), pages 116-118, March.
  3. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(2), pages 119-130, June.
  4. Roth, Alvin E, 1977. "The Shapley Value as a von Neumann-Morgenstern Utility," Econometrica, Econometric Society, Econometric Society, vol. 45(3), pages 657-64, April.
  5. Einy, Ezra, 1988. "The shapley value on some lattices of monotonic games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 15(1), pages 1-10, February.
  6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 589-614, May.
  7. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp421, The Center for the Study of Rationality, Hebrew University, Jerusalem.
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