چکیده:
The Shapley value, one of the most common solution concepts of cooperative game theory is
defined and axiomatically characterized in different game-theoretic models. Certainly, the
Shapley value can be used in interesting sharing cost/reward problems in the Operations
Research area such as connection, routing, scheduling, production and inventory situations. In
this paper, we focus on the Shapley value for cooperative games, where the set of players is
finite and the coalition values are interval grey numbers. The central question in this paper is
how to characterize the grey Shapley value. In this context, we present two alternative
axiomatic characterizations. First, we characterize the grey Shapley value using the properties
of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley
value by using the grey dividends.
خلاصه ماشینی:
"Alternative Axiomatic Characterizations of the Grey Shapley Value Sirma Zeynep Alparslan Goka, Osman Palancia, Mehmet Onur Olguna a Süleyman Demirel University, Faculty of Arts and Sciences, Department of Mathematics, Isparta, Turkey Abstract defined and axiomatically characterized in different game-theoretic models.
In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers.
It is characterized for cooperative games with a finite set and where coalition values are real numbers (Shapley, 1971, Aumann and Hart, 2002, Roth, 1988).
In the sequel, the Shapley value has captured much attention being extended in new game theoretic models and widely applied for solving reward/cost sharing problems the Operations Research and other related fields (see Baker, 1965, Borm et al.
In this study, we provide alternative axiomatic characterizations of the grey Shapley value on an additive cone of cooperative grey games inspired by the Shapley’s axiomatic characterization (see Alparslan Gök et al.
This paper focuses on the properties of the grey Shapley value and axiomatically characterizes it on an additive cone of cooperative grey games1.
, 2014, it is shown that the grey Shapley value satisfies additivity, efficiency, symmetry and dummy player properties on the class of grey size monotonic games.
By the above theorem we see that the strong monotonicity provides a simple characterization of the grey Shapley value without resorting to the usual additivity and dummy player properties.
The restriction to the class of size monotonic games is imposed by the need to establish efficiency of interval marginal vectors, and consequently of the grey Shapley value."