We propose an extension of the Ehrenfeucht-Fraïssé game able to deal with logics augmented with Lindström quantifiers. We describe three different games with varying balance between simplicity and ease of use.
Haber, S., & Shelah, S. (2015). An extension of the Ehrenfeucht-Fraïssé game for first order logics augmented with Lindström quantifiers. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9300, pp. 226–236). Springer Verlag. https://doi.org/10.1007/978-3-319-23534-9_13