The perils of selling online: Manufacturer competition, channel conflict, and consumer preferences

Abstract

Internet channels have grown rapidly in recent years due to advances in information technology. However, many leading manufacturers opt not to sell online. In this paper, we construct a theoretical model with competing manufacturers and an active retailer to explain this market phenomenon. We document the possibility of asymmetric channel structure despite the ex ante symmetry between the manufacturers. Moreover, the increasing prominence of online shopping behaviors does not necessarily lead to the increased adoption of Internet channels. The prevalence of dual-channel strategies can be regarded as a form of prisoners’ dilemma, and the manufacturers may intentionally intensify the product or channel substitution to escape from this undesirable outcome. We explain how demand expansion and competition mitigation drive these unintended consequences and provide some general guidelines for the managerial choice of channel structures.

Appendix

In this appendix, we provide the detailed equilibrium analysis. We find it more convenient to discuss the equilibrium characterizations before proving our propositions.

1.1 A.1 Equilibrium characterizations under different channel structures

By backward induction, we shall first derive the demand functions based on the consumer’s utility maximization (stage 4). Afterwards, we can then determine the retailer’s pricing strategy (stage 3) and the manufacturers’ pricing decisions (stage 2) and finally return to the first stage for the equilibrium channel structure. In the main text, we have discussed the case (B, I), and the equilibrium outcomes are summarized below:

(B, I)
Wholesale prices	$w_{1}^{\ast }\gamma ^=\frac {[4-\beta (2-\gamma ^{2})-\beta ^{2}(2+\gamma ^{2})]\alpha _{\textrm {I}}}{8-\beta ^{2}(2+3\gamma ^{2})}$
	$w_{2}^{\ast }=\frac {(1-\beta )(4+2\beta -\beta ^{2}\gamma ^{2})\alpha _{\textrm {I}}}{8-\beta ^{2}(2+3\gamma ^{2})}$
Selling prices	$p_{\textrm {I1}}^{\ast }=\frac {[24-4\beta -\beta ^{2}(8+9\gamma ^{2})]\alpha _{\textrm {I}}-\gamma [ 8-\beta ^{2}(2+3\gamma ^{2})]\alpha _{\textrm {D}}}{4[8-\beta ^{2}(2+3\gamma ^{2})]}$
	$p_{\textrm {I2}}^{\ast }=\frac {[24-4\beta +\beta ^{3}\gamma ^{2}-2\beta ^{2}(4+5\gamma ^{2})]\alpha _{\textrm {I}}-\beta \gamma [ 8-\beta ^{2}(2+3\gamma ^{2})]\alpha _{\textrm {D}}}{4[8-\beta ^{2}(2+3\gamma ^{2})]}$
	$p_{\textrm {D1}}^{\ast }=\frac {[8-\beta ^{2}(2+3\gamma ^{2})]\alpha _{\textrm {D}}-\beta (2+\beta )\gamma \alpha _{\textrm {I}}}{16-\beta ^{2}(4+6\gamma ^{2})}$
Quantities	$q_{\textrm {I1}}^{\ast }=\frac {[8-5\beta ^{2}\gamma ^{2}+4\beta (1+\gamma ^{2})-\beta ^{3}\gamma ^{2}(3+2\gamma ^{2})]\alpha _{\textrm {I}}-(1+\beta )\gamma [ 8-\beta ^{2}(2+3\gamma ^{2})]\alpha _{\textrm {D}}}{4(1+\beta )(1-\gamma ^{2})[8-\beta ^{2}(2+3\gamma ^{2})]}$
	$q_{\textrm {I2}}^{\ast }=\frac {(4+2\beta -\beta ^{2}\gamma ^{2})\alpha _{\textrm {I}}}{2(1+\beta )[8-\beta ^{2}(2+3\gamma ^{2})]}$
	$q_{\textrm {D1}}^{\ast }=\frac {(2-\gamma ^{2})\alpha _{\textrm {D}}-\gamma \alpha _{\textrm {I}}}{4(1-\gamma ^{2})}$
Feasibility condition	$\frac {\gamma }{2-\gamma ^{2}}\leq \frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}\leq \frac {8-5\beta ^{2}\gamma ^{2}+4\beta (1+\gamma ^{2})-\beta ^{3}\gamma ^{2}(3+2\gamma ^{2})}{(1+\beta )\gamma [ 8-\beta ^{2}(2+3\gamma ^{2})]}$

The feasibility condition is derived as follows. Note that the quantities must be nonnegative ($q_{\textrm {I1}}^{\ast }\geq 0$, $q_{\textrm {I2}}^{\ast }\geq 0$, and $q_{\textrm {D1}}^{\ast }\geq 0$. These sign restrictions give rise to the following feasibility conditions:

$$\frac{\gamma }{2-\gamma^{2}}\leq \frac{\alpha_{\textrm{D}}}{\alpha_{\textrm{I}}}\leq \frac{ 8-5\beta^{2}\gamma^{2}+4\beta \left(1+\gamma^{2}\right)- \beta^{3}\gamma^{2}\left(3+2\gamma^{2}\right)}{\left(1+\beta \right) \gamma \left[ 8-\beta^{2}\left(2+3\gamma^{2}\right)\right]}. $$

Given this condition, $p_{\textrm {I1}}^{\ast }-w_{1}^{\ast }\geq 0$, $p_{\textrm {I2}}^{\ast }-w_{2}^{\ast }\geq 0$, and $p_{\textrm {D1}}^{\ast }\geq 0$. Because $w_{1}^{\ast }\geq 0$ and $w_{2}^{\ast }\geq 0$ always hold, $p_{\textrm {I1}}^{\ast }\geq 0$ and $p_{\textrm {I2}}^{\ast }\geq 0$ are automatically satisfied. If this feasibility is violated, no equilibrium can be sustained in this subgame with the specified channel structure.

Since the procedures for the other five subgames are the same as that in the main text, we omit the details and simply present the equilibrium outcomes under these channel structures below.

(I, I)
Wholesale prices	$w_{1}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {I}}}{2-\beta }$
	$w_{2}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {I}}}{2-\beta }$
Selling prices	$p_{\textrm {I1}}^{\ast }=\frac {(3-2\beta )\alpha _{\textrm {I}}}{2(2-\beta )}$
	$p_{\textrm {I2}}^{\ast }=\frac {(3-2\beta )\alpha _{\textrm {I}}}{2(2-\beta )}$
Quantities	$q_{\textrm {I1}}^{\ast }=\frac {\alpha _{\textrm {I}}}{2(2-\beta )(1+\beta )}$
	$q_{\textrm {I2}}^{\ast }=\frac {\alpha _{\textrm {I}}}{2(2-\beta )(1+\beta )}$
Feasibility condition	N/A

(D, D)
Selling prices	$p_{\textrm {D1}}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {D}}}{2-\beta }$
	$p_{\textrm {D2}}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {D}}}{2-\beta }$
Quantities	$q_{\textrm {D1}}^{\ast }=\frac {\alpha _{\textrm {D}}}{2+2\beta -\beta ^{2}}$
	$q_{\textrm {D2}}^{\ast }=\frac {\alpha _{\textrm {D}}}{2+2\beta -\beta ^{2}}$
Feasibility condition	N/A

(B, B)
Wholesale prices	$w_{1}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {I}}}{2-\beta }$
	$w_{2}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {I}}}{2-\beta }$
Selling prices	$p_{\textrm {I1}}^{\ast }=\frac {(3-2\beta )\alpha _{\textrm {I}}-\gamma \alpha _{\textrm {D}}}{2(2-\beta )}$
	$p_{\textrm {I2}}^{\ast }=\frac {(3-2\beta )\alpha _{\textrm {I}}-\gamma \alpha _{\textrm {D}}}{2(2-\beta )}$
	$p_{\textrm {D1}}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {D}}}{2-\beta }$
	$p_{\textrm {D2}}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {D}}}{2-\beta }$
Quantities	$q_{\textrm {I1}}^{\ast }=\frac {\alpha _{\textrm {I}}-\gamma \alpha _{\textrm {D}}}{2(2+\beta -\beta ^{2})(1-\gamma ^{2})}$
	$q_{\textrm {I2}}^{\ast }=\frac {\alpha _{\textrm {I}}-\gamma \alpha _{\textrm {D}}}{2(2+\beta -\beta ^{2})(1-\gamma ^{2})}$
	$q_{\textrm {D1}}^{\ast }=\frac {(2-\gamma ^{2})\alpha _{\textrm {D}}-\gamma \alpha _{\textrm {I}}}{2(2+\beta -\beta ^{2})(1-\gamma ^{2})}$
	$q_{\textrm {D2}}^{\ast }=\frac {(2-\gamma ^{2})\alpha _{\textrm {D}}-\gamma \alpha _{\textrm {I}}}{2(2+\beta -\beta ^{2})(1-\gamma ^{2})}$
Feasibility condition	$\frac {\gamma }{2-\gamma ^{2}}\leq \frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}\leq \frac {1}{\gamma }$

(D, I)
Wholesale prices	$w_{2}^{\ast }=\frac {(4-3\beta ^{2}\gamma ^{2})\alpha _{\textrm {I}}-\beta \gamma (2-\beta ^{2}\gamma ^{2})\alpha _{\textrm {D}}}{8-5\beta ^{2}\gamma ^{2}}$
Selling prices	$p_{\textrm {I2}}^{\ast }=\frac {3(4-3\beta ^{2}\gamma ^{2})\alpha _{\textrm {I}}-3\beta \gamma (2-\beta ^{2}\gamma ^{2})\alpha _{\textrm {D}}}{2(8-5\beta ^{2}\gamma ^{2})}$
	$p_{\textrm {D1}}^{\ast }=\frac {(4-3\beta ^{2}\gamma ^{2})\alpha _{\textrm {D}}-\beta \gamma \alpha _{\textrm {I}}}{8-5\beta ^{2}\gamma ^{2}}$
Quantities	$q_{\textrm {I2}}^{\ast }=\frac {(4-3\beta ^{2}\gamma ^{2})\alpha _{\textrm {I}}-\beta \gamma (2-\beta ^{2}\gamma ^{2})\alpha _{\textrm {D}}}{2(1-\beta ^{2}\gamma ^{2})(8-5\beta ^{2}\gamma ^{2})}$
	$q_{\textrm {D1}}^{\ast }=\frac {(4-3\beta ^{2}\gamma ^{2})(2-\beta ^{2}\gamma ^{2})\alpha _{\textrm {D}}-\beta \gamma (2-\beta ^{2}\gamma ^{2})\alpha _{\textrm {I}}}{2(1-\beta ^{2}\gamma ^{2})(8-5\beta ^{2}\gamma ^{2})}$
Feasibility condition	$\frac {\beta \gamma }{4-3\beta ^{2}\gamma ^{2}}\leq \frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}\leq \frac {4-3\beta ^{2}\gamma ^{2}}{\beta \gamma (2-\beta ^{2}\gamma ^{2})}$

(B, D)
Wholesale prices	$w_{1}^{\ast }=\frac {(2-\beta )\alpha _{\textrm {I}}-\beta \gamma \alpha _{\textrm {D}}}{2(2-\beta )}$
Selling prices	$p_{\textrm {I1}}^{\ast }=\frac {3(2-\beta )\alpha _{\textrm {I}}-(2+\beta )\gamma \alpha _{\textrm {D}}}{4(2-\beta )}$
	$p_{\textrm {D1}}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {D}}}{2-\beta }$
	$p_{\textrm {D2}}^{\ast }=\frac {(1-\beta )\alpha _{\textrm {D}}}{2-\beta }$
Quantities	$q_{\textrm {I1}}^{\ast }=\frac {\alpha _{\textrm {I}}-\gamma \alpha _{\textrm {D}}}{4(1-\gamma ^{2})}$
	$q_{\textrm {D1}}^{\ast }=\frac {[4-(2-\beta +\beta ^{2})\gamma ^{2}]\alpha _{\textrm {D}}-(2-\beta )(1+\beta )\gamma \alpha _{\textrm {I}}}{4(2-\beta )(1+\beta )(1-\gamma ^{2})}$
	$q_{\textrm {D2}}^{\ast }=\frac {\alpha _{\textrm {D}}}{(2-\beta )(1+\beta )}$
Feasibility condition	$\frac {(2-\beta )(1+\beta )\gamma }{4-(2-\beta +\beta ^{2})\gamma ^{2}}\leq \frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}\leq \frac {1}{\gamma }$

1.2 A.2 Equilibrium channel structure

To pin down the equilibrium channel structure, we have to compare the manufacturers’ payoffs across different subgames. We shall maintain all the feasibility conditions such that all the channel structures generate a candidate market equilibrium.² After some routine algebra, the joint feasibility conditions across the six channel structures can be summarized as

$$\begin{array}{@{}rcl@{}} \frac{(2-\beta )(1+\beta )\gamma }{4-\left(2-\beta +\beta^{2}\right)\gamma^{2}}\leq \frac{\alpha_{\textrm{D}}}{\alpha_{\textrm{I}}} \leq \min \left\{\frac{1}{\gamma },\frac{8-5\beta^{2}\gamma^{2}+4\beta \left(1+\gamma^{2}\right)- \beta^{3}\gamma^{2}\left(3+2\gamma^{2}\right) }{(1+\beta )\gamma \left[ 8 -\beta^{2}\left(2+3\gamma^{2}\right)\right]}\right\}. \\ \end{array} $$

(3)

1.2.1 A.2.1 Possible equilibrium channel structures

Based on the manufacturers’ payoffs, we can identify three equilibrium channel structures: (B, B), (B, I), and (D, I). Consider (B, B) first. Given that manufacturer 2 chooses to sell through both channels, if manufacturer 1 also chooses B, his payoff is $\frac {(1-\beta )[\alpha _{\textrm {I}}^{2}-2\gamma \alpha _{\textrm {I}}\alpha _{\textrm {D}}+(2-\gamma ^{2})\alpha _{\textrm {D}}^{2}]}{ 2(2-\beta )^{2}(1+\beta )(1-\gamma ^{2})}$. We can then compare this payoff with manufacturer 1’s payoffs under (D, B) and (I, B). Choosing D is a dominated strategy from manufacturer 1’s perspective, and choosing I gives rise to a lower payoff if and only if

$$\frac{(1-\beta )\left[\alpha_{\textrm{I}}^{2}-2\gamma \alpha_{\textrm{I}}\alpha_{\textrm{D}}+ \left(2-\gamma^{2}\right)\alpha_{\textrm{D}}^{2}\right]}{2\left(2-\beta \right)^{2}\left(1+\beta \right) \left(1-\gamma^{2}\right)}\geq \frac{ \left(1-\beta \right)\left(4+2\beta -\beta^{2}\gamma^{2}\right)^{2}\alpha_{\textrm{I}}^{2}}{2\left(1+\beta \right)\left[8-\beta^{2}\left(2+3\gamma^{2}\right)\right]^{2}}. $$

Likewise, we can characterize the equilibrium conditions for structures (B, I) and (D, I).

1.2.2 A.2.2 Other channel structures

Let us first show that (I, I) cannot be sustained as an equilibrium. Suppose that manufacturer 2 chooses I. If manufacturer 1 chooses I, his payoff is $\frac {\left (1-\beta \right )\alpha _{\textrm {I}}^{2}}{2\left (2-\beta \right )^{2}\left (1+\beta \right )}$. On the other hand, if he chooses B (i.e., sells through both channels), his payoff is

$$ \begin{array}{lll} &&\frac{\left[4-\beta \left(2-\gamma ^{2}\right)-\beta ^{2}\left(2+\gamma ^{2}\right)\right]\alpha _\textrm{I}}{ 8-\beta ^{2}\left(2+3\gamma ^{2}\right)}\\[2pt] &&{\kern1pc} \times\frac{\left\{ \begin{array}{c} \left[ 8-5\beta ^{2}\gamma ^{2}+4\beta \left(1+\gamma ^{2}\right)-\beta ^{3}\gamma ^{2} \left(3+2\gamma ^{2}\right)\right]\alpha _\textrm{I} \\[2pt] -\left(1+\beta\right)\gamma \left[8-\beta ^{2}\left(2+3\gamma ^{2}\right)\right]\alpha _\textrm{D} \end{array} \right\} }{4\left(1+\beta\right)\left(1-\gamma ^{2}\right)\left[8-\beta ^{2}\left(2+3\gamma ^{2}\right)\right]} \\[2pt] &&{\kern1pc}+\frac{\left[8-\beta ^{2}\left(2+3\gamma ^{2}\right)\right]\alpha _\textrm{D}-\beta \left(2+\beta \right)\gamma \alpha _\textrm{I}}{16-\beta ^{2}\left(4+6\gamma ^{2}\right)} \frac{\left(2-\gamma ^{2}\right)\alpha_\textrm{D}-\gamma \alpha_\textrm{I}}{4\left(1-\gamma ^{2}\right)}. \end{array} $$

Straightforward algebra shows that the latter is always larger. To see this, we can write down the difference between the two in the following form:

$$A_{1}\alpha_{\textrm{D}}^{2}-A_{2}\alpha_{\textrm{I}}\alpha_{\textrm{D}}+A_{3}\alpha_{\textrm{I}}^{2}, $$

where {$A_{j}$}’s are some constants. We can verify that $A_{1}<0$ and $A_{2}^{2}-4A_{1}A_{3}\leq 0$. Thus, the above term $A_{1}\alpha _{\textrm {D}}^{2}-A_{2}\alpha _{\textrm {I}}\alpha _{\textrm {D}}+A_{3}\alpha _{\textrm {I}}^{2}$ is always negative. This implies that (I, I) is not an equilibrium because choosing B is a profitable deviation for manufacturer 1. Likewise, we can also compare the manufacturers’ payoffs and show that neither of (D, D) and (B, D) can be an equilibrium.

1.2.3 A.2.3 Comparative statics

We now examine the impact of changing the parameters ($\alpha _{\textrm {D}}$, $\alpha _{\textrm {I}}$, $\beta$, and $\gamma$) on the manufacturers’ profits. We start with the scenario (B, B) and consider the influence of $\gamma$. Recall that $\pi _{\textrm {M1}}(\textrm {B},~\textrm {B})=\pi _{\textrm {M2}}(\textrm {B},~\textrm {B})=\frac {(1-\beta )[\alpha _{\textrm {I}}^{2}-2\gamma \alpha _{\textrm {I}}\alpha _{\textrm {D}}+(2-\gamma ^{2})\alpha _{\textrm {D}}^{2}]}{ 2(2-\beta )^{2}(1+\beta )(1-\gamma ^{2})}$. Thus,

$$\frac{\partial \pi_{\textrm{M1}}\left(\textrm{B},~\textrm{B}\right)}{\partial \gamma }=\frac{\left(1-\beta \right)\gamma \alpha_{\textrm{I}}^{2}}{\left(2-\beta \right)^{2}\left(1+\beta \right)\left(1-\gamma^{2}\right)^{2}}\left(\frac{\alpha_{\textrm{D}}}{\alpha_{\textrm{I}}}-\frac{1}{\gamma }\right)\left(\frac{\alpha_{\textrm{D}}}{\alpha_{\textrm{I}}}-\gamma \right). $$

By Eq. 3, $\frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}-\frac {1}{\gamma }\leq 0$ and $\gamma \geq \frac {(2-\beta )(1+\beta )\gamma }{4-(2-\beta +\beta ^{2})\gamma ^{2}}$. Thus, when $\frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}\geq \gamma$, $\frac {\partial \pi _{\textrm {M1}}(\textrm {B},~\textrm {B})}{\partial \gamma }\leq 0$; when $\frac {\alpha _{\textrm {D}}}{\alpha _{\textrm {I}}}\leq \gamma$, $\frac {\partial \pi _{\textrm {M1}}(\textrm {B},~\textrm {B})}{\partial \gamma }\geq 0$. This suggests that even within the same (equilibrium) channel structure, the decision of channel substitution is nontrivial.

Now, we examine the influence of $\beta$. We find that

$$\frac{\partial \pi_{\textrm{M1}}\left(\textrm{B},~\textrm{B}\right)}{\partial \beta }=\frac{-\left(1-\beta +\beta^{2}\right) }{\left(2-\beta \right)^{3}\left(1+\beta \right)^{2}\left(1-\gamma^{2}\right)}\left[\alpha_{\textrm{I}}^{2}-2\gamma \alpha_{\textrm{I}}\alpha_{\textrm{D}}+\left(2-\gamma^{2}\right)\alpha_{\textrm{D}}^{2}\right]\leq 0 $$

since $\alpha _{\textrm {I}}^{2}-2\gamma \alpha _{\textrm {I}}\alpha _{\textrm {D}}+(2-\gamma ^{2})\alpha _{\textrm {D}}^{2}\geq 0$ always holds by Eq. 3. We can also derive the influence of $\beta$ under the other equilibrium channel structure (D, I), where

$$\begin{array}{@{}rcl@{}} \pi_{\textrm{M1}}\left({\textrm{D}},~{\textrm{I}}\right)&=&\frac{\left(2-\beta^{2}\gamma^{2}\right)\left[\left(4-3\beta^{2}\gamma^{2}\right)\alpha_{\textrm{D}}-\beta \gamma \alpha_{\textrm{I}}\right]^{2}}{2\left(1-\beta^{2}\gamma^{2}\right)\left(8-5\beta^{2}\gamma^{2}\right)^{2}},\\ \pi_{\textrm{M2}}\left({\textrm{D}},~{\textrm{I}}\right)&=&\frac{\left[\left(4-3\beta^{2}\gamma^{2}\right)\alpha_{\textrm{I}}-\beta \gamma \left(2-\beta^{2}\gamma^{2}\right)\alpha_{\textrm{D}}\right]^{2}}{2\left(1-\beta^{2}\gamma^{2}\right)\left(8-5\beta^{2}\gamma^{2}\right)^{2}}, \end{array} $$

and likewise for the changes of $\alpha _{\textrm {D}}$ and $\alpha _{\textrm {I}}$ under the two channel structures (B, B) and (D, I). We find that in general, the results are monotone for a given channel structure. However, a change of $\beta$, $\alpha _{\textrm {D}}$, or $\alpha _{\textrm {I}}$ may induce the equilibrium channel structure to switch from (D, I) to (B, B), and as we have argued above, the manufacturers become worse off under (B, B). Thus, all kinds of product strategies have nontrivial economic consequences as stated in the main text.