Table 2 Incumbent’s optimal strategy... | Emerald Publishing

Table 2

Incumbent’s optimal strategy with high 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 $\overset{̅}{R} \leq R < \overset{═}{R}$	$X^{*} = \frac{α - c}{2 ϕ - θ} - \frac{3 {(β R)}^{\frac{1}{2}}}{2 ϕ - θ}$	$x^{*} = \frac{2 θ {(β R)}^{\frac{1}{2}} - (θ - ϕ) (α - c)}{2 β ϕ}$
Entry is blockaded if $R \geq \overset{═}{R}$	$X^{*} = \frac{α - c}{2 β + θ}$	$x^{} = \frac{α - c}{2 β + θ}, y^{} = 0$

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 $\overset{̅}{R} \leq R < \overset{═}{R}$	$X^{*} = \frac{α - c}{2 ϕ - θ} - \frac{3 {(β R)}^{\frac{1}{2}}}{2 ϕ - θ}$	$x^{*} = \frac{2 θ {(β R)}^{\frac{1}{2}} - (θ - ϕ) (α - c)}{2 β ϕ}$
Entry is blockaded if $R \geq \overset{═}{R}$	$X^{*} = \frac{α - c}{2 β + θ}$	$x^{} = \frac{α - c}{2 β + θ}, y^{} = 0$

Source(s): Table by author