A second approach takes an internal perspective by asking whether, for a fixed set of states or types, the agents are making any substantive assumptions about what their opponents know or believe. The idea is to identify (in a given model) a set of possible conjectures about the players. For example, in a knowledge structure based on a set of states \(W\) this might be the set of all subsets of \(W\) or the set definable subsets of \(W\) in some suitable logical language. A space is said to be complete if each agent correctly takes into account each possible conjecture about her opponents. A simple counting argument shows that there cannot exist a complete structure when the set of conjectures is all subsets of the set of states (Brandenburger 2003). However, there is a deeper result here which we discuss below.