There are different ways to understand what it means for a structure to minimize the substantive assumptions about the players’ higher-order information. We do not attempt a complete overview of this interesting literature here (see Brandenburger &amp; Keisler (2006: sec. 11) and Siniscalchi (2008: sec. 3) for discussion and pointers to the relevant results). One approach considers the space of all (Harsanyi type-/Kripke-/epistemic-plausibility-) structures and tries to find a single structure that, in some suitable sense, “contains” all other structures. Such a structure, often called called a universal structure (or a terminal object in the language of category theory), if it exists, incorporates any substantive assumption that an analyst can imagine. Such structure have been shown to exists for Harsanyi type spaces (Mertens &amp; Zamir 1985; Brandenburger &amp; Dekel 1993). For Kripke structures, the question has been answered in the negative (Heifetz &amp; Samet 1998; Fagin, Geanakoplos, Halpern, &amp; Vardi 1999; Meier 2005), with some qualifications regarding the language that is used to describe them (Heifetz 1999; Roy &amp; Pacuit 2013).