 In terms of matching logical languages, this suggest a multi-modal approach, with \([\approx_i]\) ranging over i’s possible choices, and \([\equiv_i]\) representing her uncertainty about the opponents, see van Benthem, Pacuit, and Roy (2011). Moreover, when considering games rather than game forms, this picture needs to be enriched with a third feature, viz. preference modalities \([\preceq_i]\), see  Section 3.