## 5 Numerical Examples
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Parameter** & \(\mathbf{\omega^{**}}\) & \(\mathbf{p^{**}}\) & \(\mathbf{q^{**}}\) & \(\mathbf{n^{**}}\) & \(\mathbf{Q^{**}}\) & \(\mathbf{TP^{**}_{\text{CTF}}}\) & \(\mathbf{TP^{**}_{\text{CTF}}}\) & \(\mathbf{E^{**}_{\text{v}}}\) & \(\mathbf{E^{**}_{\text{v}}}\) \\ \hline \multirow{6}{*}{\(\hat{A}_{R}\)} & 24 & 39.5662 & 90.0110 & 161.711 & 3 & 485.133 & 9375.31 & 9312.03 & 202.025 & 252.476 \\  & 27 & 39.5524 & 90.0128 & 162.049 & 3 & 486.147 & 9375.38 & 9310.13 & 201.863 & 256.221 \\  & 30 & 39.5397 & 90.0145 & 162.385 & 3 & 487.155 & 9375.44 & 9308.23 & 201.702 & 259.951 \\  & 33 & 39.5282 & 90.0162 & 162.721 & 3 & 488.163 & 9375.49 & 9306.34 & 201.541 & 263.664 \\  & 36 & 39.5179 & 90.0179 & 163.057 & 3 & 489.171 & 9375.54 & 9304.45 & 201.379 & 267.362 \\ \hline \multirow{6}{*}{\(\hat{v}\)} & 0.8 & 38.1841 & 89.9787 & 162.581 & 3 & 487.743 & 9385.64 & 9328.94 & 202.744 & 220.000 \\  & 0.9 & 38.8734 & 89.9966 & 162.483 & 3 & 487.449 & 9380.53 & 9318.56 & 202.207 & 240.061 \\  & 1.0 & 39.5397 & 90.0145 & 162.385 & 3 & 487.155 & 9375.44 & 9308.23 & 201.702 & 259.951 \\  & 1.1 & 40.1846 & 90.0032 & 162.893 & 3 & 486.867 & 9370.35 & 9297.94 & 201.225 & 279.770 \\  & 1.2 & 40.8093 & 90.0501 & 162.193 & 3 & 486.579 & 9365.28 & 9287.69 & 200.773 & 299.522 \\ \hline \multirow{6}{*}{\(\hat{h}_{b}\)} & 0.040 & 39.5192 & 90.0142 & 162.439 & 3 & 487.317 & 9375.59 & 9308.52 & 201.692 & 259.386 \\  & 0.045 & 39.5294 & 90.0144 & 162.412 & 3 & 487.236 & 9375.51 & 9308.38 & 201.697 & 259.668 \\  & 0.050 & 39.5397 & 90.0145 & 162.385 & 3 & 487.155 & 9375.44 & 9308.23 & 201.702 & 259.951 \\  & 0.055 & 39.5500 & 90.0146 & 162.359 & 3 & 487.077 & 9375.36 & 9308.09 & 201.707 & 260.233 \\  & 0.060 & 39.5603 & 90.0147 & 162.332 & 3 & 486.996 & 9375.29 & 9307.94 & 201.712 & 260.516 \\ \hline \multirow{6}{*}{\(\hat{C}_{T}\)} & 2.4 & 39.5422 & 90.0141 & 162.318 & 3 & 486.954 & 9375.4249 & 9308.6097 & 201.734 & 259.206 \\  & 2.7 & 39.5409 & 90.0143 & 162.352 & 3 & 487.056 & 9375.4307 & 9308.4202 & 201.718 & 259.579 \\  & 3.0 & 39.5397 & 90.0145 & 162.385 & 3 & 487.155 & 9375.4364 & 9308.2308 & 201.702 & 259.951 \\  & 3.3 & 39.5395 & 90.0146 & 162.419 & 3 & 487.257 & 9375.4421 & 9308.0141 & 201.686 & 260.323 \\  & 3.6 & 39.5379 & 90.0148 & 162.453 & 3 & 487.359 & 9375.447 & 9307.8521 & 201.670 & 260.695 \\ \hline \multirow{6}{*}{\(\hat{A}_{M}\)} & 0.040 & 39.4741 & 90.0127 & 162.395 & 3 & 487.185 & 9375.95 & 9309.26 & 201.751 & 257.965 \\  & 0.045 & 39.5069 & 90.0136 & 162.390 & 3 & 487.170 & 9375.69 & 9308.75 & 201.726 & 258.958 \\ \cline{1-1}  & 0.050 & 39.5397 & 90.0145 & 162.385 & 3 & 487.155 & 9375.44 & 9308.23 & 201.702 & 259.951 \\ \cline{1-1}  & 0.050 & 39.5397 & 90.0147 & 162.387 & 3 & 487.140 & 9375.18 & 9307.72 & 201.677 & 260.943 \\ \cline{1-1}  & 0.060 & 39.6052 & 90.0163 & 162.376 & 3 & 487.128 & 9374.93 & 9307.20 & 201.653 & 261.936 \\ \hline \multirow{6}{*}{\(\hat{A}_{M}\)} & 40 & 39.2757 & 90.0147 & 162.387 & 3 & 487.161 & 9377.50 & 9308.25 & 197.738 & 260.173 \\  & 45 & 39.4082 & 90.0146 & 162.386 & 3 & 487.158 & 9376.47 & 9308.24 & 199.720 & 260.061 \\ \cline{1-1}  & 50 & 39.5397 & 90.0145 & 162.385 & 3 & 487.155 & 9375.44 & 9308.23 & 201.702 & 259.951 \\ \cline{1-1}  & 55 & 39.674 & 90.0144 & 162.384 & 3 & 487.152 & 9374.40 & 9308.22 & 203.683 & 259.842 \\ \cline{1-1}  & 60 & 39.8003 & 90.0143 & 162.383 & 3 & 487.149 & 9373.37 & 9308.21 & 205.063 & 295.735 \\ \hline \multirow{6}{*}{\(\hat{S}\)} & 80 & 39.0082 & 90.0148 & 162.390 & 3 & 487.170 & 9379.57 & 9308. **Example 3**. : _A sensitivity analysis revealing the effects of changes in the retailer's and manufacturer's parameters on the optimal equilibrium solutions. The data used are the same as in Example 1, and the computational results are presented in Tables 4 and 5. Table 4 presents the sensitivity analysis with respect to the retailer's parameters, from which these observations can be made:_  
1.