Table 1.

Special cases

Scenario	$\beta (v)$	$c_y(v)$	$\delta (v)$	$\rho (v)$	$v^{*}$
TR	$\frac{({\beta }_0-{\beta }_1)v}{v+v_0}+{\beta }_1$	$c_0$ (constant)	0	$\frac{{\rho }_0{v}_3}{v+v_2}$	$\infty$
CM	${\beta }_0$ (constant)	$\frac{c_0{v}_1}{v+v_1}$	${\delta }_{0}v$	0	0
CT	$\frac{({\beta }_0-{\beta }_1)v}{v+v_0}+{\beta }_1$	$\frac{c_0{v}_1}{v+v_1}$	0	0	$v_t=\frac{-{\beta }_1{v}_0+\sqrt{v_0({\beta }_0-{\beta }_1)({\beta }_0{v}_1-{\beta }_1{v}_0)}}{{\beta }_0}$
RM	${\beta }_0$ (constant)	$c_0$ (constant)	${\delta }_{0}v$	$\frac{{\rho }_0{v}_3}{v+v_2}$	$v_d=\max \left(0,-v_2+\sqrt{\frac{{\rho }_0{v}_3}{{\delta }_0}}\right)$
CR	${\beta }_0$ (constant)	$\frac{c_0{v}_1}{v+v_1}$	0	$\frac{{\rho }_0{v}_3}{v+v_2}$	Eq. (14)
TM	$\frac{({\beta }_0-{\beta }_1)v}{v+v_0}+{\beta }_1$	$c_0$ (constant)	${\delta }_{0}v$	0	Eq. (15)