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

By Willson [1993], partially defined cooperative games (PDGs in short) are first considered. A PDG is a cooperative game in which the worth of some coalitions is unknown. We investigated superadditive games and Shapley values on a class of PDGs in Masuya [2016]. We showed that the set of the superadditive full games that can be obtained from a given PDG is a polytope and showed all its extreme points (Theorem 2, Masuya [2016]). However, it is not correct despite being a very important theorem in the paper. However, in this paper, we consider alternative approaches to resolve this problem. JEL Classification Code: C710