In Multi-stage stochastic programming, we write the constraints that for scenarios $s$ and $s^{\prime}$ which have the same trajectory up to time $t$, should take the same value. That is, $$ x_{t,s} = x_{t,s^{\prime}} \quad \quad \forall t, s,s^{\prime} \in S: \: \: (\xi_{1}^s,\dots,\xi_{t-1}^s)=(\xi_{1}^{s^{\prime}},\dots,\xi_{t-1}^{s^{\prime}}) $$
I thought that for all decision variables except the first stage. For example, if $y_{ts},z_{ts}$ are used in different stages, I should write nonanticipativity constraints for all of them. However, in some papers, nonanticipativity constraints are used for just a subset of variables, like $x_{ts}$. Could you please let me know how we should decide to include a variable in nonanticipativity constraints or not.
