Variable

Stackelberg game

Partnership game

$p^{*}$

$\frac{2\theta }{3\beta }$

$\frac{\theta }{2\beta }$

$a^{*}$

$\frac{k^2{\theta }^4}{144{\beta }^2}$

$\frac{k^2{\theta }^4}{64{\beta }^2}$

$w^{*}$

$\frac{\theta }{3\beta }$

$t^{*}$

$\frac{1}{3}$

$D^{*}$

$\frac{k^2{\theta }^3}{36\beta }$

$\frac{k^2{\theta }^3}{16\beta }$

${\pi }_m^{\ast }$

$\frac{k^2{\theta }^4}{144{\beta }^2}$

${\pi }_r^{\ast }$

$\frac{k^2{\theta }^4}{216{\beta }^2}$

${\pi }_{m+r}^{\ast }$

$\frac{5k^2{\theta }^4}{432{\beta }^2}$

$\frac{k^2{\theta }^4}{64{\beta }^2}$