On the Convexity of Step Out – Step in Sequencing Games

The main result of this paper is the convexity of Step out - Step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas, Borm, and Quant (2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an arbitrary coalition in a SoSi sequencing game. In particular, we use that in determining an optimal processing order of a coalition S U {i}, the algorithm can start from the optimal processing order found for coalition S and thus all information on this optimal processing order of S can be used