Table 1 Incumbent’s optimal strategy... | Emerald Publishing

Table 1

Incumbent’s optimal strategy with generic entry

	Entry	Incumbent’s profit-maximizing first-period output level	Second-period output at equilibrium
$θ = 0$	Entry if $R < \frac{1}{β} {(\frac{α - c}{3})}^{2}$	$x^{*} = \frac{α - c}{2 β}$	$x^{} + y^{} = \frac{2 (α - c)}{3 β}$
$θ = 0$	No entry if $R \geq \frac{1}{β} {(\frac{α - c}{3})}^{2}$	$x^{*} = \frac{α - c}{2 β}$	$x^{*} = \frac{α - c}{2 β}$
$0 < θ < 2 β$	Entry is accommodated if $R < \overset{̅}{R}$	$X^{*} = \frac{α - c}{2} \frac{9 β - 2 θ}{(3 β + θ) (3 β - θ)}$	$x^{} + y^{} = (α - c)) \frac{3 (2 β - θ)}{(3 β + θ) (3 β - θ)}$
	Entry is preempted if $\overset{̅}{R} \leq R < \overset{═}{R}$	$X^{*} = \frac{α - c}{θ} - \frac{3 {(β R)}^{\frac{1}{2}}}{θ}$	$x^{*} = \frac{3}{2} {(\frac{R}{β})}^{\frac{1}{2}}$
	Entry is blockaded if $R \geq \overset{═}{R}$	$X^{*} = \frac{α - c}{2 β + θ}$	$x^{*} = \frac{α - c}{2 β + θ}$
$θ \geq 2 β$	Entry is blockaded	$X^{*} = \frac{α - c}{2 β}$	$x^{*} = 0$

	Entry	Incumbent’s profit-maximizing first-period output level	Second-period output at equilibrium
$θ = 0$	Entry if $R < \frac{1}{β} {(\frac{α - c}{3})}^{2}$	$x^{*} = \frac{α - c}{2 β}$	$x^{} + y^{} = \frac{2 (α - c)}{3 β}$
$θ = 0$	No entry if $R \geq \frac{1}{β} {(\frac{α - c}{3})}^{2}$	$x^{*} = \frac{α - c}{2 β}$	$x^{*} = \frac{α - c}{2 β}$
$0 < θ < 2 β$	Entry is accommodated if $R < \overset{̅}{R}$	$X^{*} = \frac{α - c}{2} \frac{9 β - 2 θ}{(3 β + θ) (3 β - θ)}$	$x^{} + y^{} = (α - c)) \frac{3 (2 β - θ)}{(3 β + θ) (3 β - θ)}$
	Entry is preempted if $\overset{̅}{R} \leq R < \overset{═}{R}$	$X^{*} = \frac{α - c}{θ} - \frac{3 {(β R)}^{\frac{1}{2}}}{θ}$	$x^{*} = \frac{3}{2} {(\frac{R}{β})}^{\frac{1}{2}}$
	Entry is blockaded if $R \geq \overset{═}{R}$	$X^{*} = \frac{α - c}{2 β + θ}$	$x^{*} = \frac{α - c}{2 β + θ}$
$θ \geq 2 β$	Entry is blockaded	$X^{*} = \frac{α - c}{2 β}$	$x^{*} = 0$

Source(s): Table by author