 It should be said that imperfect information challenges this approach to game algebra. For instance, one may have to decompose a larger game into smaller subgames where agents need not know which of these subgames they are in. Game algebras with imperfect information have been studied in the context of Boolean Games (Harrenstein et al. 2001). A recent power-based game algebra with operations encoding imperfect information, showing some analogies with IF logic (Mann, Sandu, &amp; Sevenster 2011) can be found in van Benthem, Bezhanishvili, and Enqvist (2019b).