Balancedness of sequencing games with multiple parallel machines

We provide simple constructive proofs of balancedness of classes of m-PS (in-Parallel Sequencing) games, which arise from sequencing situations with in parallel machines. This includes the setting that is studied by Calleja et al. (2001) and Calleja et al. (2002), who provided a complex constructive proof and a simple non-constructive proof of balancedness of a restricted class of 2-PS games, respectively. Furthermore, we provide a counterexample to illustrate that our balancedness results cannot be extended to a general setting.