Abstract
In the classical approach to cooperative games it is assumed that the worth of every coalition is known. However, in the real world problems there may be situations in which the amount of information is limited and consequently the worth of some coalitions are unknown. The games corresponding to those problems are called partially defined cooperative games (PDGs in short). The Shapley values for PDGs proposed so far need so much time to calculate them. Since the Shapley value plays an important role in applications of cooperative game theory to real world problems, we should consider methods to obtain the Shapley value or its approximation efficiently. We propose an approximated Shapley value which can be obtained efficiently. An axiom system of the proposed value is also shown.
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