Table 2 Results of equilibrium decision-making in the case of without channel integration and with channel integration.
Without channel integration (\(j=n\)) | With channel integration (\(j=i\)) | |
|---|---|---|
\({{w}^{j}}^{* }\) | \(p-\frac{{k}_{r}(4{k}_{o}{t}^{2}+\sigma )}{2{k}_{r}-{k}_{o}}\) | \(p-\frac{{k}_{r}(16{k}_{o}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}+{(\alpha +\beta -2\alpha \beta )}^{2}\sigma )}{(2{k}_{r}-{k}_{o}){(\alpha +\beta -2\alpha \beta )}^{2}}\) |
\({{s}_{r}^{j}}^{* }\) | \(\frac{4{k}_{o}{t}^{2}+\sigma }{4(2{k}_{r}-{k}_{o})t}\) | \(\frac{16{k}_{o}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}+{(\alpha +\beta -2\alpha \beta )}^{2}\sigma }{8(2{k}_{r}-{k}_{o})(1-\alpha )\alpha (\alpha +\beta -2\alpha \beta )t}\) |
\({{s}_{o}^{j}}^{* }\) | \(\frac{4{k}_{o}{k}_{r}{t}^{2}+({k}_{o}-{k}_{r})\sigma }{4(2{k}_{r}-{k}_{o})t}\) | \(\frac{16{k}_{o}{k}_{r}{t}^{2}{(1-\alpha )}^{2}{\alpha }^{2}-({k}_{r}-{k}_{o}){(\alpha +\beta -2\alpha \beta )}^{2}\sigma }{8{k}_{o}(2{k}_{r}-{k}_{o})(1-\alpha )\alpha (\alpha +\beta -2\alpha \beta )t}\) |
\({{D}_{r}^{j}}^{* }\) | \(\frac{{k}_{r}(4{k}_{o}{t}^{2}+\sigma )}{8{k}_{o}(2{k}_{r}-{k}_{o}){t}^{2}}\) | \(\frac{\left(\begin{array}{c}8{{k}_{o}}^{2}{t}^{2}{\left(1-\alpha \right)}^{2}\alpha \left(\alpha -\beta \right)+16{k}_{o}{k}_{r}{t}^{2}{\left(1-\alpha \right)}^{3}\alpha \beta \\ +{k}_{r}\left(1-\beta \right){\left(\alpha +\beta -2\alpha \beta \right)}^{2}\sigma \end{array}\right)}{16{k}_{o}(2{k}_{r}-{k}_{o}){\left(1-\alpha \right)}^{2}\alpha (\alpha +\beta -2\alpha \beta ){t}^{2}}\) |
\({{D}_{o}^{j}}^{* }\) | \(\frac{4{k}_{o}\left(3{k}_{r}-2{k}_{o}\right){t}^{2}-{k}_{r}\sigma }{8{k}_{o}(2{k}_{r}-{k}_{o}){t}^{2}}\) | \(\frac{\left(\begin{array}{c}8{k}_{o}{t}^{2}\left(1-\alpha \right){\alpha }^{2}\left(2{k}_{r}\left(\alpha +2\beta -3\alpha \beta \right)-{k}_{o}\left(\alpha +3\beta -4\alpha \beta \right)\right)\\ -{k}_{r}\beta {\left(\alpha +\beta -2\alpha \beta \right)}^{2}\sigma \end{array}\right)}{16{k}_{o}(2{k}_{r}-{k}_{o}){t}^{2}(1-\alpha ){\alpha }^{2}(\alpha +\beta -2\alpha \beta )}\) |
\({{D}_{c}^{j}}^{* }\) | / | \(\frac{(\alpha -\beta )(16{k}_{o}({k}_{r}-{k}_{o}){(1-\alpha )}^{2}{\alpha }^{2}{t}^{2}-{k}_{r}{(\alpha +\beta -2\alpha \beta )}^{2}\sigma )}{16{k}_{o}(2{k}_{r}-{k}_{o}){\left(1-\alpha \right)}^{2}{\alpha }^{2}{t}^{2}(\alpha +\beta -2\alpha \beta )}\) |
\({{\pi }_{r}^{j}}^{* }\) | \(\frac{{k}_{r}{(4{k}_{o}{t}^{2}+\sigma )}^{2}}{16{k}_{o}(2{k}_{r}-{k}_{o}){t}^{2}}\) | \(\frac{{k}_{r}{(16{k}_{o}{(1-\alpha )}^{2}{\alpha }^{2}{t}^{2}+{(\alpha +\beta -2\alpha \beta )}^{2}\sigma )}^{2}}{64{k}_{o}(2{k}_{r}-{k}_{o}){(1-\alpha )}^{2}{\alpha }^{2}{t}^{2}{(\alpha +\beta -2\alpha \beta )}^{2}}\) |
\({{\pi }_{m}^{j}}^{* }\) | \(p-c-{\varLambda }_{1}\) | \(p-c-{\varLambda }_{2}\) |
