The Restricted Core for Totally Positive Games with Ordered Players

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems, such as river games, queueing games and auction games, the game is totally positive (i.e., all dividends are nonnegative), and there is some hierarchical ordering of the players. In this paper we introduce the 'Restricted Core' for such 'games with ordered players' which is based on the distribution of 'dividends' taking into account the hierarchical ordering of the players. For totally positive games this solution is always contained in the 'Core', and contains the well-known 'Shapley value' (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions). For special orderings it equals the Core, respectively Shapley value. We provide an axiomatization and apply this solution to river games.