Axiomatizations of the proportional Shapley value

  • Manfred BesnerEmail author


We present new axiomatic characterizations of the proportional Shapley value, a weighted TU-value with the worths of the singletons as weights. The presented characterizations are proportional counterparts to the famous characterizations of the Shapley value by Shapley (Contributions to the theory of games, vol. 2. Princeton University Press, Princeton, pp 307–317, 1953b) and Young (Cost allocation: methods, principles, applications. North Holland Publishing Co, 1985a). We introduce two new axioms, called proportionality and player splitting, respectively. Each of them makes a main difference between the proportional Shapley value and the Shapley value. If the stand-alone worths are plausible weights, the proportional Shapley value is a convincing alternative to the Shapley value, for example in cost allocation. Especially, the player splitting property, which states that players’ payoffs do not change if another player splits into two new players who have the same impact to the game as the original player, justifies the use of the proportional Shapley value in many economic situations.


Cost allocation Dividends Proportional Shapley value (Weighted) Shapley value Proportionality Player splitting 



We would like to thank André Casajus, Winfried Hochstättler, Jörg Homberger, Frank Huettner, Hans Peters, and especially an anonymous referee for their helpful comments and suggestions.


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Authors and Affiliations

  1. 1.Department of Geomatics, Computer Science and MathematicsHFT Stuttgart, University of Applied SciencesStuttgartGermany

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