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Two extensions of Young's axiomatization for the Shapley value

Summary: Two extensions of Young's axiomatization for
the Shapley value
Anna B. Khmelnitskaya
SPb Institute for Economics and Mathematics Russian Academy of Sciences,
1 Tchaikovsky St., 191187 St.Petersburg, Russia,
e-mail: a.khmelnitskaya@math.utwente.nl
Among single-valued solutions usually called values the most famous and the
most appealing is the Shapley value [3]. Different axiomatizations for the Shapley
value defined on the entire space of games with fixed set of players are known.
Two main of them are the classical one given by Shapley [3] and that of Young
[6]. The original Shapley's axiomatization exploits the additivity axiom that
being a very beautiful mathematical statement does not express any fairness
property. The axiomatization of Young that characterizes the Shapley value by
marginality, efficiency, and symmetry appears to be more attractive since all the
axioms present different reasonable properties of fair division. The goal of this
paper is to present two extensions of the Young's axiomatization for the Shapley
Fist, not always we consider the entire space of games. Sometimes due to
different reasons we restrict consideration to some subclass of games, e.g. to
nonnegative or positive games, to simple games, to convex games, to superad-


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering