The interplay between quality improvement and information acquisition in an E-commerce supply chain

Abstract

This study investigates an e-commerce supply chain comprising a supplier and an online retailer, wherein the supplier determines the quality improvement of products and the online retailer decides whether or not to acquire information on consumer preference. Consumer preference is ex-ante unknown to both the supplier and online retailer but can be resolved by the online retailer’s information acquisition behavior. We consider two widely adopted information acquisition strategies, namely, the committed acquisition strategy and contingent acquisition strategy, which differ in whether the online retailer’s information acquisition decision is made prior to or after the supplier’s quality improvement decision. We find that, under either strategy, the online retailer acquires information only when the cost of information acquisition is relatively small. Moreover, compared with the contingent one, the committed acquisition scheme boosts the online retailer’s motivation to gain information. Additionally, by comparing firms’ equilibrium profits under these two acquisition strategies, we uncover that the supplier always prefers the committed acquisition scheme. However, the online retailer’s preference toward these two information acquisition strategies is not unidirectional, that is, the online retailer prefers either the committed or the contingent strategy. Specifically, the online retailer is indifferent between these two acquisition strategies when the acquisition cost is either sufficiently low or high; otherwise, when the cost of information acquisition is moderate, the online retailer will shift her strategy from the contingent strategy to the committed strategy as the acquisition cost increases.

Appendix

1.1 Proposition 1

Proof

By comparing the equilibrium quality improvement level with acquisition and non-acquisition under the committed acquisition strategy, we demonstrate that $m^{D} = \frac{{5(1 - \alpha )(\rho ^{2} \alpha ^{2} - 2\rho (4 - \rho )\alpha + (\rho + 2)^{2} )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)}}$ is always greater than $m^{N} = \frac{{(1 - \alpha )(\rho ^{2} \alpha ^{2} - 2\rho (4 - \rho )\alpha + (\rho + 2)^{2} )}}{{2k((1 + \alpha )^{2} \rho - 8\alpha + 8)}}$.□

1.2 Proposition 2

Proof

If and only if $\Pi _{r}^{D} \ge \Pi _{r}^{N}$, then the online retailer will opt to obtain consumers’ quality preference information. Thus, we can derive that the online retailer will opt to obtain consumers’ quality preference information when $c \le \tilde{c}_{1} (\alpha ,\rho ,k) = \frac{{9(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$; otherwise, the online retailer will opt to obtain consumers’ quality preference information.□

1.3 Corollary 1

Proof

By calculating the first derivative of $\tilde{c}_{1} (\alpha ,\rho ,k)$ to $\rho$, we have $\Delta = \frac{{\partial \tilde{c}_{1} (\alpha ,\rho ,k)}}{{\partial \rho }} = - \frac{\begin{gathered} 9( - 1 + \alpha )[8\alpha ^{8} ( - 4 + \rho )\rho ^{4} + \alpha ^{9} \rho ^{5} - 2(2 + \rho )^{3} ( - 10 + 35\rho + 2\rho ^{2} ) \hfill \\ + 2\alpha ^{7} \rho ^{3} (192 - 79\rho + 12\rho ^{2} ) + 2\alpha ^{6} \rho ^{2} ( - 1020 + 352\rho - 85\rho ^{2} + 14\rho ^{3} ) \hfill \\ + 2\alpha ^{5} \rho (2056 + 1220\rho - 704\rho ^{2} + 153\rho ^{3} - 7\rho ^{4} ) \hfill \\ + \alpha ^{3} (1856 + 22752\rho - 6512\rho ^{2} + 640\rho ^{3} + 438\rho ^{4} - 112\rho ^{5} ) \hfill \\ + \alpha (192 + 3984\rho + 3816\rho ^{2} + 384\rho ^{3} - 330\rho ^{4} - 27\rho ^{5} ) \hfill \\ - 2\alpha ^{2} (832 + 6880\rho + 1948\rho ^{2} - 1312\rho ^{3} + 119\rho ^{4} + 38\rho ^{5} ) \hfill \\ - 2\alpha ^{4} (272 + 8256\rho - 3216\rho ^{2} + 1440\rho ^{3} - 395\rho ^{4} + 42\rho ^{5} )] \hfill \\ \end{gathered} }{{32k[8 + 2\alpha ( - 4 + \rho ) + \rho + \alpha ^{2} \rho ]^{4} }}$. By calculating $\Delta$, we derive that the thresholds of $\tilde{\alpha }$, $\rho _{1} (\alpha )$, and $\rho _{2} (\alpha )$ exist. When $0 < \alpha \le \frac{1}{3}$ and $0 < \rho < \rho _{1} (\alpha )$, when $\frac{1}{3} < \alpha \le \tilde{\alpha }$ and $0 < \rho \le \frac{{6\alpha - 2}}{{(1 + \alpha )^{2} }}$, or when $\tilde{\alpha } < \alpha < 1$ and $\rho _{2} (\alpha ) < \rho \le \frac{{6\alpha - 2}}{{(1 + \alpha )^{2} }}$, $\Delta = \frac{{\partial \tilde{c}_{1} (\alpha ,\rho ,k)}}{{\partial \rho }} > 0$. Otherwise, $\Delta = \frac{{\partial \tilde{c}_{1} (\alpha ,\rho ,k)}}{{\partial \rho }} < 0$.□

1.4 Corollary 2

Proof

According to the equilibrium upstream supplier’s and online retailer’s profits with acquisition and non-acquisition, we demonstrate that the online retailer’s profits $\frac{{25(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} - c$ decrease linearly with acquisition cost when $c \le \tilde{c}_{1} (\alpha ,\rho ,k)$. Moreover, the retailer’s profits $\frac{{(1 - \alpha )T(\alpha ,\rho )}}{{4k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$ is independent of acquisition cost when $c > \tilde{c}_{1} (\alpha ,\rho ,k)$. Thus, the online retailer’s profits tend to decrease along with information acquisition cost. For the supplier, when $c > \tilde{c}_{1} (\alpha ,\rho ,k)$, his profits have a decreasing jump. Therefore, the profit of the supplier also decreases along with information acquisition cost.□

1.5 Proposition 3

Proof

Assuming that the online retailer opts to obtain information on consumers’ quality preference, when $\theta = \theta _{L}$, the profit of the online retailer is $\frac{{K(\alpha ,\rho )}}{{4((1 + \alpha )^{2} - 8\alpha + 8)^{2} }}m - c$, and when $\theta = \theta _{H}$, the profit of the online retailer is $\frac{{K(\alpha ,\rho )}}{{((1 + \alpha )^{2} - 8\alpha + 8)^{2} }}m - c$. However, when the online retailer refuses to obtain such information, her profit is $\frac{{K(\alpha ,\rho )}}{{2((1 + \alpha )^{2} - 8\alpha + 8)^{2} }}m$. By comparing these equilibrium profits with the equilibrium profit under non-acquisition, if and only if $c \le \frac{{K(\alpha ,\rho )}}{{8((1 + \alpha )^{2} - 8\alpha + 8)^{2} }}m$, then the online retailer will opt to obtain consumers’ quality preference information. Building on the optimal information acquisition decision of online retailers, we analyze the decision of the upstream supplier regarding the product quality improvement level. We consider the following scenarios:

• (1) If the downstream retailer opts to obtain information about consumers’ quality preferences, then the upstream supplier solves the following optimization problem:

  $$ \begin{aligned} & Max\Pi _{s}^{D} (m) = \underbrace {{\frac{1}{2}\left(\frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)}}{{(1 + \alpha )^{2} \rho - 8\alpha + 8}}m - \frac{{km^{2} }}{2}\right)}}_{{\theta = \theta _{H} }} + \underbrace {{\frac{1}{2}\left(\frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)}}{{4((1 + \alpha )^{2} \rho - 8\alpha + 8)}}m - \frac{{km^{2} }}{2}\right)}}_{{\theta = \theta _{L} }} \\ & \qquad s.t.\;c \le \frac{{K(\alpha ,\rho )}}{{8((1 + \alpha )^{2} - 8\alpha + 8)^{2} }}m. \\ \end{aligned} $$

We can obtain the optimal solution to the optimization problem as follows: if $c \le \frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, then $m^{\# } = \frac{{5(1 - \alpha )(\rho ^{2} \alpha ^{2} - 2\rho (4 - \rho )\alpha + (\rho + 2)^{2} )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)}}$; otherwise, $m^{\# } = \frac{{(1 + \alpha )^{2} \rho - 8\alpha + 8}}{{K(\alpha ,\rho )}}c$. Therefore, when $c \le \frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, the profits of the upstream supplier are $\Pi _{s}^{\# } = \frac{{25(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{128k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}$; otherwise, $\Pi _{s}^{\# } = \frac{{(1 + \alpha )^{2} \rho - 8\alpha + 8)(5(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho ) - 32ck((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} )}}{{(K(\alpha ,\rho ))^{2} }}c$.

• (2) If the downstream retailer refuses to obtain information about consumers’ quality preference, then the upstream supplier solves the following optimization problem:

  $$ \begin{aligned} & Max\Pi _{s}^{N} (m) = \frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)}}{{2((1 + \alpha )^{2} \rho - 8\alpha + 8)}}m - \frac{{km^{2} }}{2} \\ & \quad s.t.\;c > \frac{{K(\alpha ,\rho )}}{{8((1 + \alpha )^{2} - 8\alpha + 8)^{2} }}m. \\ \end{aligned} $$

We can obtain the optimal solution to the optimization problem as follows: if $c > \frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho )}}{{2k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}$, then $m^{*} = \frac{{(1 - \alpha )(\rho ^{2} \alpha ^{2} - 2\rho (4 - \rho )\alpha + (\rho + 2)^{2} )}}{{2k((1 + \alpha )^{2} \rho - 8\alpha + 8)}}$; otherwise, $m^{{\text{*}}} = \frac{{(1 + \alpha )^{2} \rho - 8\alpha + 8}}{{K(\alpha ,\rho )}}c$. Therefore, when $c > \frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho )}}{{2k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}$, the profits of the upstream supplier are $\Pi _{s}^{*} = \frac{{(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}$; otherwise, $\Pi _{s}^{{\text{*}}} = \frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)}}{{2((1 + \alpha )^{2} \rho - 8\alpha + 8)}} - \frac{{8ck((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}{{K(\alpha ,\rho )}}$.□

The following inequality holds:

$\frac{{25(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{128k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }} \ge \frac{{(1 + \alpha )^{2} \rho - 8\alpha + 8)(5(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho ) - 32ck((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} )}}{{(K(\alpha ,\rho ))^{2} }}c$; $\frac{{(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }} \ge \frac{{(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)}}{{2((1 + \alpha )^{2} \rho - 8\alpha + 8)}} - \frac{{8ck((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}{{K(\alpha ,\rho )}}$; $\frac{{25(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{128k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }} \ge \frac{{(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }}$.

Therefore, we can derive that (1) when $c \le \tilde{c}_{2} (\alpha ,\rho ,k) = \frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, the online retailer opts to obtain consumers’ quality preference information; (2) when $\frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} = \tilde{c}_{2} (\alpha ,\rho ,k) < c \le \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, the upstream supplier induces the online retailer to obtain information about consumers’ quality preferences by improving product quality level; and (3) when $c > \tilde{c}_{3} (\alpha ,\rho ,k)$, the upstream supplier induces the online retailer not to obtain consumers’ quality preference information.

1.6 Corollary 3

The process of the proof is similar to that of Corollary 1. Therefore, we omit the related discussion here for brevity.

1.7 Corollary 4

Proof

In accordance with Proposition 3, for the supplier, when $c \le \tilde{c}_{2} (\alpha ,\rho ,k) = \frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, his profits are independent of information acquisition cost. When $\frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} = \tilde{c}_{2} (\alpha ,\rho ,k) < c \le \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, $\frac{{\partial \Pi _{s}^{\# } }}{{\partial c}} = \frac{{((1 + \alpha )^{2} \rho - 8\alpha + 8)(64ck((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} - 5(1 - \alpha )T(\alpha ,\rho )}}{{K(\alpha ,\rho )}} < 0$, but when $c > \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, his profits are independent of information acquisition cost. Given that supplier profit is a continuous function of information disclosure cost, this profit tends to decrease along with information acquisition cost.□

For the online retailer, when $c \le \tilde{c}_{2} (\alpha ,\rho ,k) = \frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, her profit decreases linearly along with acquisition cost. When $\frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} = \tilde{c}_{2} (\alpha ,\rho ,k) < c \le \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, her profits increase linearly along with information acquisition cost. However, there is a declining jump in profits for downstream retailers when $c = \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$. Moreover, when $c > \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, the profits of the online retailer are independent of information acquisition cost.

1.8 Propositions 4 and 5

Comparing the results for Propositions 1 to 3 yields Propositions 4 and 5. Therefore, we omit the related discussion here for simplicity.

1.9 Proposition 6

Proof

According to Propositions 2 and 3, when $c \le \tilde{c}_{2} (\alpha ,\rho ,k) = \frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$ or $c > \tilde{c}_{1} (\alpha ,\rho ,k) = \frac{{9(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, the profits of the downstream retailer, upstream suppliers, and the whole supply chain differ between the two acquisition strategies. We only focus on $\tilde{c}_{2} (\alpha ,\rho ,k) < c \le \tilde{c}_{1} (\alpha ,\rho ,k)$ below:

• (1) When $\frac{{5(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} = \tilde{c}_{2} (\alpha ,\rho ,k) < c \le \tilde{c}_{3} (\alpha ,\rho ,k) = \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, $\Pi _{r}^{{\text{*}}} - \Pi_{r}^{\# } {\text{ = }}\frac{{25(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} - 5c \le 0$, $\begin{gathered} \Pi _{s}^{*} - \Pi _{s}^{\# } = \frac{{25(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{128k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }} \hfill \\ - \frac{{(1 + \alpha )^{2} \rho - 8\alpha + 8)(5(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho ) - 32ck((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} )}}{{(K(\alpha ,\rho ))^{2} }}c \ge 0 \hfill \\ \end{gathered}$, $(\Pi _{r}^{*} + \Pi _{s}^{*} ) - (\Pi _{r}^{\# } + \Pi _{s}^{\# } ) < 0$.

• (2) When $\frac{{(1 - \alpha )T(\alpha ,\rho )}}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} = \tilde{c}_{3} (\alpha ,\rho ,k) < c \le \tilde{c}_{1} (\alpha ,\rho ,k) = \frac{{9(1 - \alpha )T(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }}$, $\Pi _{r}^{*} - \Pi _{r}^{\# } = \frac{{25(1 - \alpha )((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)K(\alpha ,\rho )}}{{64k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} - \frac{{(1 - \alpha )T(\alpha ,\rho )}}{{4k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{3} }} - c \ge 0$, $\Pi _{s}^{*} - \Pi _{s}^{\# } = \frac{{25(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{128k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }} - \frac{{(1 - \alpha )^{2} ((1 + \alpha )^{2} \rho ^{2} + 4(1 - 2\alpha )\rho + 4)^{2} }}{{8k((1 + \alpha )^{2} \rho - 8\alpha + 8)^{2} }} > 0$, $(\Pi _{r}^{*} + \Pi _{s}^{*} ) - (\Pi _{r}^{\# } + \Pi _{s}^{\# } ) > 0$.□