On axiomatizations of the Shapley value for assignment games |
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| Institution: | 1. VU University, Department of Econometrics and Tinbergen Institute, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands;2. Corvinus University of Budapest, Department of Mathematics, 1093, Budapest, Fovám tér 13-15, Hungary;3. MTA-BCE “Lendület” Strategic Interactions Research Group, 1093, Budapest, Fovám tér 13-15, Hungary;4. Department of Business and Economics, University of Pecs, Hungary;1. Université de Franche-Comté, CRESE, 30 Avenue de l’Observatoire, 25009 Besançon, France;2. HHL Leipzig Graduate School of Management, Jahnallee 59, 04109 Leipzig, Germany;3. LSI Leipziger Spieltheoretisches Institut, Leipzig, Germany;4. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France;1. Chair of Economics and Information Systems, HHL Leipzig Graduate School of Management, Jahnallee 59, 04109 Leipzig, Germany;2. LSI Leipziger Spieltheoretisches Institut, Leipzig, Germany;1. Department of Computer Science, Northwestern University, USA;2. Department of Computer Science, University of Southern California, Los Angeles, CA 90089, USA;3. Department of Computer Science, Columbia University, USA;1. Department of Economics, Aomori Public University, 153-4, Yamazaki, Goshizawa, Aomori 030-0196, Japan;2. Department of Economics, Ryutsu Keizai University, 120, Ryugasaki, Ibaraki 301-8555, Japan;3. Faculty of Economics, Keio University, 2-15-45, Mita, Minato-ku, Tokyo 108-8345, Japan;4. School of Political Science and Economics, Waseda University, 1-6-1, Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan |
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| 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. |
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| Keywords: | Game theory Assignment game Shapley value Graph game Submarket efficiency Valuation fairness |
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