 Further notions of bisimulation take an even coarser perspective on the games’ move structure, for instance by allowing to contract zones where the same player moves several times in a row. Finally, dropping all information about players and their choices, games can be compared by the sequences of moves they admit. This purely observational notion, known as trace equivalence in computation, may, however, be less relevant in the context of games. An alternative approach to coarsening focuses on the players’ powers to control outcomes, cf.  Section 2.5  and van Benthem, Bezhanishvili and Enqvist (2019a).