Recently, applications of cooperative game theory to economic allocation problems have gained popularity. To understand these applications better, economic theory studies the similarities and differences between them. The purpose of this paper is to investigate a special class of cooperative games that generalizes some recent economic applications with a similar structure. These are so-called line-graph games being cooperative TU-games in which the players are linearly ordered. Examples of situations that can be modeled like this are sequencing situations, water distribution situations and political majority voting. The main question in cooperative game models of economic situations is how to allocate the earnings of coalitions among the players. We apply the concept of Harsanyi solution to line-graph games. We define four properties that each selects a unique Harsanyi solution from the class of all Harsanyi solutions. One of these solutions is the well-known Shapley value which is widely applied in economic models. We apply these solutions to the economic situations mentioned above. sharing system, Harsanyi solution, line-graph game