Table 3 Incumbent’s optimal strategy... | Emerald Publishing

Table 3

Incumbent’s optimal strategy with low cross-resistance (ϕ<θ/2)

Entry	Incumbent’s profit maximizing first-period output level	Second-period output at equilibrium
Entry is accommodated if $R < \overset{̅}{R}$	$X^{*} = \frac{α - c}{2 β} \frac{9 β^{2} - 2 β (2 θ - ϕ)}{9 β^{2} - {(2 θ - ϕ)}^{2}}$	$x^{} = \frac{α - c}{3 β} - \frac{(2 θ - ϕ) X}{3 β}, y^{} = \frac{α - c}{3 β} - \frac{(2 ϕ - θ) X}{3 β}$
Entry is pre-empted if $\overset{̅}{R} \leq R < \hat{R}$	$X^{*} = \frac{3 {(β R)}^{\frac{1}{2}}}{θ - 2 ϕ} - \frac{α - c}{θ - 2 ϕ}$	$x^{*} = \frac{2 (θ - ϕ) (α - c) - 3 θ {(β R)}^{\frac{1}{2}}}{2 β (θ - 2 ϕ)}$
Entry is blockaded if $R \geq \hat{R}$	$X^{*} = \frac{α - c}{2 β + θ}$	$x^{*} = \frac{α - c}{2 β + θ}$

Entry	Incumbent’s profit maximizing first-period output level	Second-period output at equilibrium
Entry is accommodated if $R < \overset{̅}{R}$	$X^{*} = \frac{α - c}{2 β} \frac{9 β^{2} - 2 β (2 θ - ϕ)}{9 β^{2} - {(2 θ - ϕ)}^{2}}$	$x^{} = \frac{α - c}{3 β} - \frac{(2 θ - ϕ) X}{3 β}, y^{} = \frac{α - c}{3 β} - \frac{(2 ϕ - θ) X}{3 β}$
Entry is pre-empted if $\overset{̅}{R} \leq R < \hat{R}$	$X^{*} = \frac{3 {(β R)}^{\frac{1}{2}}}{θ - 2 ϕ} - \frac{α - c}{θ - 2 ϕ}$	$x^{*} = \frac{2 (θ - ϕ) (α - c) - 3 θ {(β R)}^{\frac{1}{2}}}{2 β (θ - 2 ϕ)}$
Entry is blockaded if $R \geq \hat{R}$	$X^{*} = \frac{α - c}{2 β + θ}$	$x^{*} = \frac{α - c}{2 β + θ}$

Source(s): Table by author