The stable gain splitting rule for sequencing situations

Abstract

We study sequencing situations with a fixed initial order, linear cost functions, and extended possibilities for profitable rearrangements by coalitions to obtain associated relaxed sequencing games. We introduce an allocation rule that is guaranteed to result in a core-element for all relaxed sequencing games. This tackles the core nonemptiness issue constructively, whereas thus far nonconstructive approaches are available only. Subsequently, we provide several characterizations of this rule. The first characterization considers a property on the robustness against specific merges of players combined with a property that requires core membership for the basic sequencing game only, i.e., the game constructed without extended possibilities for rearrangements by coalitions. The second characterization resembles the original characterization of the Equal Gain Splitting rule, the only difference being an alternative switch property. Our final main result states that our rule can be obtained by the players via neighbour switches with nonnegative, position independent, gain splits.