Table 3 Equilibrium outcomes for a... | Emerald Publishing

Table 3

Equilibrium outcomes for a product-service supply chain under a manufacturer’s own industrial internet platform

	Decentralized decision-making	Centralized decision-making
$P_{s}^{D *}$	$\frac{(4 b k - 4 β^{2} - k) C_{s} + (k - C_{s} β ρ + {C_{s}}^{2} b ρ^{2}) (γ \overset{̅}{q} + a) - 4 {C_{s}}^{2} b ρ β}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}$	$\frac{- 2 {C_{s}}^{2} b β ρ + (2 b k - 2 β^{2} - k) C_{s} + (- {C_{s}}^{2} ρ^{2} b - C_{s} ρ β + k) (γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} - 4 C_{s} b β ρ + 4 b k - 2 β^{2} - k}$
$W^{*}$	$\frac{(- {C_{s}}^{2} ρ^{2} b + k - C_{s} ρ β) (γ \overset{̅}{q} + a) + C_{s} (4 k b - 4 β^{2} - k) - 4 {C_{s}}^{2} ρ β b}{- 4 {C_{s}}^{2} b^{2} ρ^{2} - 8 C_{s} ρ β b + 8 b_{2} k - 4 β^{2} - k}$	__
$i^{D *}$	$\frac{(C_{s} ρ b + β) (γ \overset{̅}{q} + a - 4 C_{s} b)}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - k}$	$\frac{(C_{s} ρ b + β) (- 2 C_{s} b + γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$P_{p}^{D *}$	$\frac{(C_{s} k + (6 k - 6 C_{s} ρ β) (γ \overset{̅}{q} + a)) b - (3 β^{2} + k + 3 ρ^{2} {C_{s}}^{2} b^{2}) (γ \overset{̅}{q} + a)}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (8 C_{s} ρ β - 8 k) b + β^{2} + k / 4)}$	$\frac{(C_{s} k + (2 k - 2 C_{s} ρ β) (γ \overset{̅}{q} + a)) b - (β^{2} + k + {C_{s}}^{2} b^{2} ρ^{2}) (γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} ρ^{2} b^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$D_{p}^{D *}$	$\frac{(2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}$	$\frac{(- {C_{s}}^{2} b^{2} ρ^{2} - 2 C_{s} ρ β b + 2 k b - β^{2}) (γ \overset{̅}{q} + a) - C_{s} b k}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$D_{s}^{D *}$	$\frac{b k (- 4 C_{s} b + γ \overset{̅}{q} + a)}{- 4 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}$	$\frac{b k (- 2 C_{s} b + γ \overset{̅}{q} + a)}{- 2 {C_{s}}^{2} b^{2} ρ^{2} + (- 4 C_{s} ρ β + 4 k) b - 2 β^{2} - k}$
$π_{m}^{D *}$	$\frac{4 {C_{s}}^{2} b^{2} k + 2 C_{s} k b (γ \overset{̅}{q} + a) - (2 b (k + C_{s} β ρ) + {C_{s}}^{2} b^{2} ρ^{2} + β^{2}) {(γ \overset{̅}{q} + a)}^{2}}{- 8 ({C_{s}}^{2} b^{2} ρ^{2} + (2 C_{s} ρ β - 2 k) b + β^{2} + k / 4)}$	__
$π_{s}^{D *}$	$\frac{{((2 k b - 2 C_{s} β ρ b - {C_{s}}^{2} b^{2} ρ^{2} - β^{2}) (γ \overset{̅}{q} + a) - C_{s} k b)}^{2}}{16 {({C_{s}}^{2} b^{2} ρ^{2} + 2 C_{s} b β ρ - 2 b k + β^{2} + k / 4)}^{2}}$	__
$π_{s c}^{D *}$	$π_{s}^{D } + π_{m}^{D }$	$\frac{(- {C_{s}}^{2} b^{2} ρ^{2} + 2 (- C_{s} ρ β b + k b) - β^{2}) {(γ \overset{̅}{q} + a)}^{2} - 2 C_{s} b k (γ \overset{̅}{q} + a) + 2 {C_{s}}^{2} b^{2} k}{- 4 {C_{s}}^{2} b^{2} ρ^{2} + (- 8 C_{s} ρ β + 8 k) b - 4 β^{2} - 2 k}$

Source(s): Authors’ own creation