On the inverse problem for a subclass of linear, symmetric and efficient values of cooperative TU games

In this paper we solve the inverse problem for each linear, symmetric, efficient and regular value (or LSER value for short). That is, given a payoff vector and a LSER value, we find all TU games such that LSER value for them is equal to the given payoff vector. Also, we characterize those linear, symmetric and efficient values that further satisfy the inessential game property.