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 et al. (Eur J Oper Res 246:894–906, 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, the algorithm can start from the optimal processing order found for any subcoalition of smaller size and thus all information on such an optimal processing order can be used.

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Keywords (Cooperative) game theory, Convexity, Relaxed sequencing games
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Journal TOP
Musegaas, M., Borm, P.E.M, & Quant, M. (2017). On the convexity of step out–step in sequencing games. TOP, 1–42. doi:10.1007/s11750-017-0455-2