# How to write nonanticipativity constraints?

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.

• Is there anybody who can help me with this question? – Katatonia Mar 29 at 4:16