Table 3 Benefit matrix of the TEGM for the central government, local government A and B.

(1,1,1)

H−C_C−M_A−M_B

−C_A + M_A

−C_B + M_B

(1,1,0)

−C_C − M_A + F_B

−C_A−R_A−δ₁W_A + M_A

−δ₁Q_B + δ₂G_B−F_B + T_B + λB

(1,0,1)

−C_C − M_B + F_A

−δ₁Q_A + δ₂G_A−F_A + T_A + λB

−C_B−R_B−δ₁W_B + M_B

(0,1,1)

H−M_A−M_B

−C_A + M_A

−C_B + M_B

(1,0,0)

−C_C + F_A + F_B

−δ₁Q_A + δ₂G_A−δ₁W_A−F_A + λB

−δ₁Q_B + δ₂G_B − δ₁W_B−F_B + λB

(0,1,0)

−M_A−F_C

−C_A−R_A − δ₁W_A + M_A

−δ₁Q_B + δ₂G_B + T_B + λB

(0,0,1)

−M_B−F_C

−δ₁Q_A + δ₂G_A + T_A + λB

−C_B−R_B−δ₁W_B + M_B

(0,0,0)

−F_C

−δ₁Q_A + δ₂G_A−δ₁W_A + λB

−δ₁Q_B + δ₂G_B−δ₁W_B + λB