Balancedness of sequencing games with multiple parallel machines

We provide simple constructive proofs of balancedness of classes of m-PS (m-Parallel Sequencing) games, which arise from sequencing situations with m parallel machines. This includes the setting that was studied by Calleja et al., 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.