Two Approaches to Estimate the Shapley Value for Convex Partially Defined Games

Satoshi Masuya ()
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Satoshi Masuya: Faculty of Business Administration, Daito Bunka University, 1-9-1, Takashimadaira, Itabashi-ku, Tokyo 175-8571, Japan

Mathematics, 2023, vol. 12, issue 1, 1-15

Abstract: In the classical approach of von Neumann and Morgenstern to cooperative games, it was assumed that the worth of all coalitions must be given. However, in real-world problems, the worth of some coalitions may be unknown. Therefore, in this study, we consider the Shapley value for convex partially defined games using two approaches. Firstly, we introduce a polytope that includes the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. The elements of this polytope are said to be the Shapley payoff vectors. Secondly, we obtain the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. Moreover, we axiomatize the proposed two values.

Keywords: cooperative game; partially defined game; Shapley value (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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