A short proof of convexity of step-out–step-in sequencing games

The Step out–Step in sequencing game is a particular example of from the framework Curiel, Perderzoli, and Tijs, where coalitions players queue may reorder themselves to improve their overall cost, under some restrictions. Musegaas, Borm Quant proved, two papers, that simple greedy algorithm correctly computes valuation coalition, convex. These proofs entail rather involved case analyses; this note, we give short both results.