1. Introduction

The following corrections need to be applied to [Reference Akbarzadeh and Mahajan1]:

1. 1. On p. 11, Equation (19) is missing a term and should be updated as follows:

   \begin{align*} D^{(h_{d,y})} & = D^{(h_{d})} - \dfrac{(1-\beta) \Phi^{(h_{d})} (c^{(h_d)} - c^{(h_{d, y})}) + \beta\rho^{\mathsf{T}}_y \Phi^{(h_{d})}_{\cdot y}D^{(h_{d})}}{1 + \beta\rho^{\mathsf{T}}_y \Phi^{(h_{d})}_{\cdot y}}, \\[5pt] N^{(h_{d,y})} & = N^{(h_{d})} - \dfrac{(1-\beta) \Phi^{(h_{d})} (h_d - h_{d, y}) + \beta\rho^{\mathsf{T}}_y \Phi^{(h_{d})}_{\cdot y}N^{(h_{d})}}{1 + \beta\rho^{\mathsf{T}}_y \Phi^{(h_{d})}_{\cdot y}}. \end{align*}
   These formulas are derived by combining Equations (8) and (18).

2. 2. On p. 15, the numbers and indices in Part 4 are incorrect and should be updated as follows:

   • For $y = 2$ , $h_{2,2} = [0, 0, 0]$ , $N^{(h_{2,2})} = [0, 0, 0]$ , and $D^{(h_{2,2})} = [\!-\!0.21, -0.22, -0.37]$ . Therefore, $\Lambda_{2,2} = \{x \in \mathcal{X} \;:\; N^{(\bar g^{(\mathcal{W}_2)}}(x) \neq N^{(h_{2,2})}(x) \} = \{1, 2, 3\}$ . Now, for each $x \in \Lambda_{2,2}$ , we compute $\mu_{2,2}(1) = \mu_{2,2}(2) = \mu_{2,2}(3) = 0.8$ . Therefore, $\mu^*_{2,2} = 0.8$ .

Now $\mu^*_{2,2} = 0.8$ . Therefore, $\mathcal{W}_3 = \{1, 2, 3\}$ and $w(2) = 0.8$ .

Some other grammatical errors and typos are highlighted below:

1. 1. On p. 6, Figure 1: The lower $D^{(h_2)}(x)$ should be changed to $D^{(h_1)}(x)$ . The updated figure is as follows:

   

2. 2. On p. 6, Lemma 1: The term ‘piecewise linear’ is repeated and should be removed from the first sentence. The updated lemma should read as follows:

   Lemma 1. For any $x \in \mathcal{X}$ , $V_\lambda(x)$ is continuous, increasing, and concave in $\lambda$ . Furthermore, when $\mathcal{X}$ is finite, $V_\lambda(x)$ is piecewise linear in $\lambda$ .

3. 3. On p. 18, proof of Lemma 5: The statement starting with ‘Now (D5) implies that …’ should be changed to ‘The assumption that $N^{(g^{(\ell)})}(x)$ is non-increasing in $\ell$ implies that ….’

4. 4. On p. 20, line 4: The second $Z^{[g]}$ should be $\tilde Z^{[g]}$ . So the line after the displayed equation should read as follows: ‘… then $Z^{[g]} = \left[\begin{array}{c@{\quad}c} 6 & 8 \\[5pt] 14 & 16 \end{array}\right]$ and $\tilde{Z}^{[g]} = \left[\begin{array}{c@{\quad}c} 5 & 8 \\[5pt] 13 & 15 \end{array}\right]$ .’

5. 5. On p. 22, line 3: Where we say ‘relative (percentage) performance improvement’, we should instead say ‘relative (percentage) performance’.