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 requires us to specify a different probability measure for each partition cell which can be quite cumbersome. Fortunately, the properties in the above definition imply that, for each agent, we can view the agent’s probability measures as arising from one probability measure through conditionalization. Formally, for each \(i\in\Agt\), agent \(i\)’s (subjective) prior probability is any element of \(p_i\in\Delta(W)\). Then, in order to define an epistemic-probability model we need only give for each agent \(i\in\Agt\), (1) a prior probability \(p_i\in\Delta(W)\) and (2) a partition \(\Pi_i\) on \(W\) such that for each \(w\in W\), \(p_i(\Pi_i(w))&gt;0\). The probability measures for each \(i\in\Agt\) are then defined by: