$w^{*}<0$

$0\le w^{*}<1$

$1\le w^{*}$

${\rho }^{*}<0$

(0,0,1)

$\left[0,\overline{w},\left(1-\overline{w}\right)\right]$

(0,1,0)

$0\le {\rho }^{*}<1$

$\left[{\rho }^{*},0,\left(1-{\rho }^{*}\right)\right]$

$\left[{\rho }^{*},w^{*}\left(1-{\rho }^{*}\right),\left(1-w^{*}\right)\left(1-{\rho }^{*}\right)\right]$

$\left[{\rho }^{*},1-{\rho }^{*},0\right]$

$1\le {\rho }^{*}$

(1,0,0)

(1,0,0)

(1,0,0)