The Shapley value without efficiency and additivity

We provide a new characterization of the Shapley value neither using the e¢ciency axiom nor the additivity axiom. In this characterization, e¢ciency is replaced by the gain-loss axiom (Einy and Haimanko, 2011, Game Econ Behav 73: 615–621), i.e., whenever the total worth generated does not change, a player can only gain at the expense of another one. Additivity and the equal treatment axiom are substituted by fairness (van den Brink, 2001, Int J Game Theory 30: 309–319) or di¤erential marginality (Casajus, 2011, Theor Decis 71: 163–174), where the latter requires equal productivity di¤erentials of two players to translate into equal payo¤ di¤erentials. The third axiom of our characterization is the standard dummy player axiom. Key Words: Shapley value; gain-loss axiom; di¤erential marginality; e¢ciency, additivity JEL code: C71, D60 AMS subject classi…cation: 91A12 yLSI Leipziger Spieltheoretisches Institut, Leipzig, Germany; e-mail: [email protected] Professur für Mikroökonomik, Wirtschaftswissenschaftliche Fakultät, Universität Leipzig, Grimmaische Str. 12, 04009 Leipzig, Germany. We are grateful to Fank Huettner for comments on this note. 1