Table 2

The equilibrium results for four strategies without government subsidies.

Results Stratege ND Stratege NJ Stratege NR Stratege NC
x ei * $ {x}_{{ei}}^{\mathrm{*}}$ 2 ψ 1 ψ 3 ψ 4 ψ 5 $ \frac{2{\psi }_1{\psi }_3{\psi }_4}{{\psi }_5}$ 2 ψ 1 ψ 3 ψ 4 ψ 5 $ \frac{2{\psi }_1{\psi }_3{\psi }_4}{{\psi }_5}$ 2 ψ 1 ψ 2 ψ 4 ψ 6 $ \frac{2{\psi }_1{\psi }_2{\psi }_4}{{\psi }_6}$ 2 ψ 1 ψ 2 ψ 4 ψ 6 $ \frac{2{\psi }_1{\psi }_2{\psi }_4}{{\psi }_6}$
x fi * $ {x}_{{fi}}^{\mathrm{*}}$ 2 ϕ 1 ϕ 3 ϕ 4 ϕ 5 $ \frac{2{\phi }_1{\phi }_3{\phi }_4}{{\phi }_5}$ 2 ϕ 1 ϕ 2 ϕ 4 ϕ 6 $ \frac{2{\phi }_1{\phi }_2{\phi }_4}{{\phi }_6}$ 2 ϕ 1 ϕ 3 ϕ 4 ϕ 5 $ \frac{2{\phi }_1{\phi }_3{\phi }_4}{{\phi }_5}$ 2 ϕ 1 ϕ 2 ϕ 4 ϕ 6 $ \frac{2{\phi }_1{\phi }_2{\phi }_4}{{\phi }_6}$
q ei * $ {q}_{{ei}}^{\mathrm{*}}$ 3 γ ψ 1 ψ 5 $ \frac{3\gamma {\psi }_1}{{\psi }_5}$ 3 γ ψ 1 ψ 5 $ \frac{3\gamma {\psi }_1}{{\psi }_5}$ 3 γ ψ 1 ψ 6 $ \frac{3\gamma {\psi }_1}{{\psi }_6}$ 3 γ ψ 1 ψ 6 $ \frac{3\gamma {\psi }_1}{{\psi }_6}$
q fi * $ {q}_{{fi}}^{\mathrm{*}}$ 3 γ ϕ 1 ϕ 5 $ \frac{3\gamma {\phi }_1}{{\phi }_5}$ 3 γ ϕ 1 ϕ 6 $ \frac{3\gamma {\phi }_1}{{\phi }_6}$ 3 γ ϕ 1 ϕ 5 $ \frac{3\gamma {\phi }_1}{{\phi }_5}$ 3 γ ϕ 1 ϕ 6 $ \frac{3\gamma {\phi }_1}{{\phi }_6}$
π Mi * $ {\pi }_{{Mi}}^{\mathrm{*}}$ γ ψ 1 2 ψ 7 ψ 5 2 + γ ϕ 1 2 ϕ 7 ϕ 5 2 $ \frac{\gamma {\psi }_1^2{\psi }_7}{{\psi }_5^2}+\frac{\gamma {\phi }_1^2{\phi }_7}{{\phi }_5^2}$ γ ψ 1 2 ψ 7 ψ 5 2 + γ ϕ 1 2 ϕ 6 $ \frac{\gamma {\psi }_1^2{\psi }_7}{{\psi }_5^2}+\frac{\gamma {\phi }_1^2}{{\phi }_6}$ γ ψ 1 2 ψ 6 + γ ϕ 1 2 ϕ 7 ϕ 5 2 $ \frac{\gamma {\psi }_1^2}{{\psi }_6}+\frac{\gamma {\phi }_1^2{\phi }_7}{{\phi }_5^2}$ γ ψ 1 2 ψ 6 + γ ϕ 1 2 ϕ 6 $ \frac{\gamma {\psi }_1^2}{{\psi }_6}+\frac{\gamma {\phi }_1^2}{{\phi }_6}$
W S * $ W{S}^{\mathrm{*}}$ 4 γ ψ 1 2 ψ 8 ψ 5 2 + 4 γ ϕ 1 2 ϕ 8 ϕ 5 2 $ \frac{4\gamma {\psi }_1^2{\psi }_8}{{\psi }_5^2}+\frac{4\gamma {\phi }_1^2{\phi }_8}{{\phi }_5^2}$ 4 γ ψ 1 2 ψ 8 ψ 5 2 + 4 γ ϕ 1 2 ϕ 8 ϕ 6 2 $ \frac{4\gamma {\psi }_1^2{\psi }_8}{{\psi }_5^2}+\frac{4\gamma {\phi }_1^2{\phi }_8}{{\phi }_6^2}$ 4 γ ψ 1 2 ψ 8 ψ 6 2 + 4 γ ϕ 1 2 ϕ 8 ϕ 5 2 $ \frac{4\gamma {\psi }_1^2{\psi }_8}{{\psi }_6^2}+\frac{4\gamma {\phi }_1^2{\phi }_8}{{\phi }_5^2}$ 4 γ ψ 1 2 ψ 8 ψ 6 2 + 4 γ ϕ 1 2 ϕ 8 ϕ 6 2 $ \frac{4\gamma {\psi }_1^2{\psi }_8}{{\psi }_6^2}+\frac{4\gamma {\phi }_1^2{\phi }_8}{{\phi }_6^2}$

Note: ψ1 = θa – c, ψ2 = 1 + η, ψ3 = 2 – η, ψ4 = h + np0, ψ 5 = 9 γ - 2 ψ 2 ψ 3 ψ 4 2 $ {\psi }_5=9\gamma -2{\psi }_2{\psi }_3{\psi }_4^2$, ψ 6 = 9 γ - 2 ψ 2 2 ψ 4 2 $ {\psi }_6=9\gamma -2{\psi }_2^2{\psi }_4^2$, ψ 7 = 9 γ - 2 ψ 3 2 ψ 4 2 , $ {\psi }_7=9\gamma -2{\psi }_3^2{\psi }_4^2,$ ψ 8 = 9 γ - ψ 3 2 ψ 4 2 , $ {\psi }_8=9\gamma -{\psi }_3^2{\psi }_4^2,$ ϕ1 = a(1 − θ) − p0 (μ + λ), ϕ2 = 1 + β, ϕ3 = 2 − β, ϕ4 = g + p0, ϕ 5 = 9 γ - 2 ϕ 2 ϕ 3 ϕ 4 2 , $ {\phi }_5=9\gamma -2{\phi }_2{\phi }_3{\phi }_4^2,$ ϕ 6 = 9 γ - 2 ϕ 2 2 ϕ 4 2 $ {\phi }_6=9\gamma -2{\phi }_2^2{\phi }_4^2$, ϕ 7 = 9 γ - 2 ϕ 3 2 ϕ 4 2 $ {\phi }_7=9\gamma -2{\phi }_3^2{\phi }_4^2$, ϕ 8 = 9 γ - ϕ 3 2 ϕ 4 2 ,   $ {\phi }_8=9\gamma -{\phi }_3^2{\phi }_4^2,\enspace $ *∈ {NDNJNRNC}.

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