 This is where the choice function \(C\) comes in: for each moment \(m\) and agent \(i, C\) yields a partitioning \(C_i^m\) of the set \(H_m\) of all histories through \(m\). An equivalence class in \(C_i^m\) is called a choice cell. (Note that two histories belonging to the same choice cell agree up to the moment in question but not necessarily later on.) If \(h\) is a history running through \(m\) we write \(C_i^m(h)\) for the choice cell of which \(h\) is a member. It is natural to associate \(C_i^m\) with the set of actions open to the agent \(i\) at \(m\), and to think of the choice cell \(C_i^m(h)\) as representing the action associated with \(h\).