Cooperative and axiomatic approaches to the knapsack allocation problem

Abstract In the knapsack problem a group of agents want to fill with several goods. Two issues must be considered. The first is decide optimally what goods select for knapsack. This issue has been studied in many papers literature on Operations Research and Management Science. second divide total revenue among agents. only few papers, this one them. For each we consider three associated cooperative games. One them (the pessimistic game) already considered literature. other two (realistic optimistic games) are defined paper. realistic games have non-empty cores but core game could empty. We then follow axiomatic approach. propose rules: based optimal solution problem. Shapley value so called game. offer characterizations both rules.