Strategic introduction of the showroom channel in a platform supply chain: how to balance cost inefficiency against information asymmetry

Abstract

To cope with the challenge caused by the lack of physical evaluation, many e-commerce platforms introduce a showroom channel, in which consumers can feel and touch products before purchasing. Based on this background, we consider there are two strategies of an e-commerce platform to introduce a showroom channel, i.e., self-build strategy and cooperation strategy. Then we build theoretical models by characterising cost inefficiency of self-build strategy and information asymmetry of cooperation strategy in the platform supply chain. Next, we derive the optimal decisions under different strategies, and investigate the advantage of different strategies. Last, we explore the strategic introduction of the showroom channel in the platform supply chain. We find the following results. (1) Under cooperation strategy, the platform can strategically design two different cooperation contracts to the retailer, i.e., full incentive contract and partial incentive contract. Moreover, the retailer may be hurt by a higher demand due to information asymmetry under cooperation strategy. (2) Self-build strategy generates information advantage and cooperation strategy brings channel advantage, which jointly affect the optimal showroom channel strategy of the platform. To be more specific, when high-type demand of the retailer is relatively high and reservation profit of the retailer is relatively low, channel advantage dominates information advantage, then the platform will choose cooperation strategy. (3) Under some conditions, the optimal strategy of the platform is not in line with the optimal ones of the whole supply chain. Then we design a side payment contract to achieve Pareto improvement.

Appendices

Appendix 1

Proof of Proposition 1

Under asymmetric information, the retailer has incentive to lie about the demand information. Then the optimal decisions of supply chain members will change. Due to backward induction, we derive the optimal decisions of the platform and the retailer when one type of the retailer pretends to be another type, which are $p_{H}^{C*} \left( {r_{L} } \right) = \frac{{a_{RH} + e_{RH} \left( {r_{L} } \right) + r_{L} }}{2}$, $p_{L}^{C*} \left( {r_{H} } \right) = \frac{{a_{RL} + e_{RH} \left( {r_{H} } \right) + r_{H} }}{2}$, $e_{RH}^{C*} \left( {r_{L} } \right) = \frac{{r_{L} }}{2}$ and $e_{RL}^{C*} \left( {r_{H} } \right) = \frac{{r_{H} }}{2}$. Taking the above decisions into the constraints in Eq. (9), we have $\pi_{RH}^{C} \left( {r_{H} ,F_{H} } \right) - \pi_{RL}^{C} \left( {r_{H} ,F_{H} } \right) = \frac{{r_{H} \left( {a_{RH} - 1} \right)}}{2} > 0$, and $\pi_{RL}^{C} \left( {r_{L} ,F_{L} } \right) - \pi_{RH}^{C} \left( {r_{L} ,F_{L} } \right) = - \frac{{r_{L} \left( {a_{RH} - 1} \right)}}{2} < 0$. Combined with the constraint in Eq. (9), we have $\pi_{RH}^{C} \left( {r_{H} ,F_{H} } \right) > \pi_{RH}^{C} \left( {r_{L} ,F_{L} } \right) > \pi_{RL}^{C} \left( {r_{L} ,F_{L} } \right) > \pi_{0}$. As a result, constraints (ICH) and (IRL) in Eq. (9) are active. Then we construct Lagrange function due to constraints in Eq. (9), which is:

$$\Phi = E\left[ {\pi_{P}^{C} } \right] + \lambda_{1} r_{H} + \lambda_{2} r_{L} + \lambda_{3} \left( {\pi_{RL}^{C} \left( {r_{L} ,F_{L} } \right) - \pi_{0} } \right) + \lambda_{4} \left( {\pi_{RH}^{C} \left( {r_{H} ,F_{H} } \right) - \pi_{RH}^{C} \left( {r_{L} ,F_{L} } \right)} \right).$$

(11)

We use KKT conditions to solve the Lagrange function in Eq. (11), which is $\frac{{\partial {\Phi }}}{{\partial r_{i} }} = 0$ ($i = H,L$), $\lambda_{k} \ge 0$ ($k = 1, 2, 3, 4$), $\frac{{\partial {\Phi }}}{{\partial \lambda_{k} }} \ge 0$ and $\lambda_{k} \frac{{\partial {\Phi }}}{{\partial \lambda_{k} }} = 0$. According to KKT conditions, we need to consider seven cases but only two sets of solutions are obtained. That is, (1) $\frac{{\partial {\Phi }}}{{\partial r_{i} }} = 0$, $\lambda_{k} = 0$ and $\frac{{\partial {\Phi }}}{{\partial \lambda_{k} }} > 0$ for $k = 1, 2, 3, 4$; (2) $\frac{{\partial {\Phi }}}{{\partial r_{i} }} = 0$, $\lambda_{k} = 0$ and $\frac{{\partial {\Phi }}}{{\partial \lambda_{k} }} > 0$ for $k = 1, 3, 4$, $\lambda_{2} > 0$ and $\frac{{\partial {\Phi }}}{{\partial \lambda_{2} }} = 0$. Organizing relevant results and conditions, we have the two contract designing strategies in Proposition 1.

Proof of Proposition 2

Comparing the optimal showroom service level among different strategies, we have:

$$e_{PL}^{S*} - e_{RL}^{CF*} = \frac{{2\left[ {\beta_{R} a_{RH} \left( {2k_{P} - 1} \right) - \beta_{P} k_{P} - 2\beta_{R} - k_{P} + 3} \right]}}{{5\left( {2k_{P} - 1} \right)\left( {1 - \beta_{R} } \right)}}$$

(12)

$$e_{PH}^{S*} - e_{RH}^{CF*} = \frac{{3\beta_{R} a_{RH} \left( {2k_{P} - 1} \right) - 3\beta_{P} k_{P} - \beta_{R} - 3k_{P} + 4}}{{5\left( {2k_{P} - 1} \right)\left( {1 - \beta_{R} } \right)}}$$

(13)

$$e_{PL}^{S*} - e_{RL}^{CP*} = \frac{1}{{2k_{P} - 1}} > 0$$

(14)

$$e_{PH}^{S*} - e_{RH}^{CP*} = \frac{{5a_{PH} - a_{RH} \left( {2k_{P} - 1} \right)}}{{5\left( {2k_{P} - 1} \right)}}$$

(15)

From Eq. (12), we know the relationship between $e_{PL}^{S*}$ and $e_{RL}^{CF*}$ depends on the sign of $\left[ {\beta_{R} a_{RH} \left( {2k_{P} - 1} \right) - \beta_{P} k_{P} - 2\beta_{R} - k_{P} + 3} \right]$, which is a linear increasing function of $a_{RH}$. Then using the property of linear increasing function, it is easy to verify the relationship between $e_{PL}^{S*}$ and $e_{RL}^{CF*}$. The remaining proofs of Proposition 2 are similar.

Proof of Proposition 3

Substituting the optimal decisions of supply chain members in different strategies into the expected profit of the platform, we have:

$$E\left[ {\pi_{P}^{S*} } \right] - E\left[ {\pi_{P}^{CF*} } \right] = \pi_{0} + Z_{1}$$

(16)

$$E\left[ {\pi_{P}^{S*} } \right] - E\left[ {\pi_{P}^{CP*} } \right] = \pi_{0} + Z_{2}$$

(17)

We can easily verify the denominator of $Z_{1}$ is greater than zero. Then we analyse the numerator of $Z_{1}$, which is a quadratic function of $a_{RH}$. Based on the property of quadratic function, we can get that when $1 < a_{RH} \le {\text{min}}\left\{ {a_{1} ,\frac{{1 + \beta_{R} }}{{2\beta_{R} }}} \right\}$, $Z_{1} \ge 0$; $\max \left\{ {a_{1} ,1} \right\} < a_{RH} \le \frac{{1 + \beta_{R} }}{{2\beta_{R} }}$, $Z_{1} < 0$. Then Proposition 3(1) is obtained. The proofs of Propositions 3(2) and 4 are similar.

Proof of Proposition 5

Substituting the expected profits of supply chain members under different strategies in Proposition 1 into Eq. (10), let $\frac{{\partial \left( {E\left[ {\pi_{R}^{CF*} } \right] - T} \right)^{\theta } \left( {E\left[ {\pi_{P}^{CF*} } \right] - E\left[ {\pi_{P}^{S*} } \right] + T} \right)^{1 - \theta } }}{\partial T} = 0$, which is given is Proposition 5.

Proof of Proposition 6

Solving the derivative of $T^{*}$ with respect to $\theta$, we can easily have the sign of $\frac{{\partial T^{*} }}{\partial \theta }$ equals to the sign of $- \Delta \pi_{SC}$. Under the improvement regions, $\Delta \pi_{SC}$ is always larger than 0, thus $\frac{{\partial T^{*} }}{\partial \theta } < 0$.

Solving the derivative of $T^{*}$ with respect to $a_{RH}$, we have:

$$\frac{{\partial T^{*} }}{{\partial a_{RH} }} = \frac{{\beta_{R} \left[ {\left( {5\theta \beta_{R} - 3\theta - 4\beta_{R} } \right)a_{RH} - 2\theta \beta_{R} + 3\beta_{R} + 1} \right]}}{{5\left( {1 - \beta_{R} } \right)}}$$

(18)

The following proof of Proposition 6(2) is similar to that of Proposition 2.