These two properties together constrain the probability measures across partition cells in a way that is consistent with conditionalization from a single prior.

Property 1 says that if \(i\) assigns a non-zero probability to state \(v\) at state \(w\) then the agent uses the same probability measure at both states. This means that the players “know” their own probability measures. The second property implies that players must assign a probability of zero to all states outside the current (hard) information cell. These models provide a very precise description of the players’ hard and soft informational attitudes. However, note that writing down a model