On consistency of reward allocation rules in sequencing situations

In this paper we consider the equal gain splitting rule and the split core. Both are solution concepts for sequencing situations and were introduced by Curiel, Pederzoli and Tijs (1989) and Hamers, Suijs, Tijs and Borm (1994) respectively. Our goal is a characterization of these solution concepts using consistency properties. However, to do this we need a more subtle look at the allocations assigned by both solution concepts. In the current definitions they assign aggregated allocations, i.e. only the total reward is assigned to each agent. To use consistency in sequencing situations, aggregated solution concepts do not provide sufficient information. What we need is a further specification of this total reward of an agent. Therefore we introduce so called non-aggregated solution concepts. A non-aggregated solution concept assigns a vector to each agent, in some way representing the specification of his total reward. Consequently, a non-aggregated solution concept assigns to each sequencing situation a matrix instead of a vector. In this paper we introduce the non-aggregated counter-parts of the equal gain splitting rule and the split core and characterize them using consistency.