Table 2. Jacobian matrix of the game model for the supplier and the retailer.

Equilibrium point	det(J)	tr(J)
O(0,0)	${\lambda }^2{c}_1^{{\beta }_1}{c}_2^{{\beta }_2}$	$-\lambda c_1^{{\beta }_1}-\lambda c_2^{{\beta }_2}$
A(1,0)	$\lambda c_1^{{\beta }_1}[n^{{\alpha }_2}+{(t_2{b}_1)}^{{\alpha }_2}-\lambda c_2^{{\beta }_2}]$	$\lambda c_1^{{\beta }_1}+[n^{{\alpha }_2}+{(t_2{b}_1)}^{{\alpha }_2}-\lambda c_2^{{\beta }_2}]$
B(0,1)	$[m^{{\alpha }_1}+{(t_1{b}_2)}^{{\alpha }_1}-\lambda c_1^{{\beta }_1}]\lambda c_2^{{\beta }_2}$	$[m^{{\alpha }_1}+{(t_1{b}_2)}^{{\alpha }_1}-\lambda c_1^{{\beta }_1}]+\lambda c_2^{{\beta }_2}$
C(1,1)	$[m^{{\alpha }_1}+{(t_1{b}_2)}^{{\alpha }_1}-\lambda c_1^{{\beta }_1}][n^{{\alpha }_2}+{(t_2{b}_1)}^{{\alpha }_2}-\lambda c_2^{{\beta }_2}]$	$-[m^{{\alpha }_1}+{(t_1{b}_2)}^{{\alpha }_1}-\lambda c_1^{{\beta }_1}]-[n^{{\alpha }_2}+{(t_2{b}_1)}^{{\alpha }_2}-\lambda c_2^{{\beta }_2}]$
D(x*,y*)	$-{\lambda }^2{c}_1^{{\beta }_1}{c}_2^{{\beta }_2}\frac{[m^{{\alpha }_1}+{(t_1{b}_2)}^{{\alpha }_1}-\lambda c_1^{{\beta }_1}][n^{{\alpha }_2}+{(t_2{b}_1)}^{{\alpha }_2}-\lambda c_2^{{\beta }_2}]}{[m^{{\alpha }_1}+{(t_1{b}_2)}^{{\alpha }_1}][n^{{\alpha }_2}+{(t_2{b}_1)}^{{\alpha }_2}]}$	0