\begin{equation}
\label{eq:delta-plus}
U^{+}{} (\mathbf{d}_{mt}, \mathbf{d}_{-mt}, \tilde{d}_{nit}) = U({\mathbf{d}_{mt} \cup \{\tilde{d}_{nit}\}},\mathbf{d}_{-mt} \setminus \{\tilde{d}_{nit}\}) - U(\mathbf{d}_{mt},\mathbf{d}_{-mt}) + \varepsilon~.
\end{equation}
