Cooperative and axiomatic approaches to the knapsack allocation problem

In the knapsack problem a group of agents want to fill a knapsack with several goods. Two issues should be considered. Firstly, to decide optimally the goods selected for the knapsack, which has been studied in many papers. Secondly, to divide the total revenue among the agents, which has been studied in few papers (including this one). We assign to each knapsack problem several cooperative games. For some of them we prove that the core is non-empty. Later, we follow the axiomatic approach. We propose two rules. The first one is based on the optimal solution of the knapsack problem. The second one is the Shapley value of the so called optimistic game. We offer axiomatic characterizations of both rules