New retail versus traditional retail in e-commerce: channel establishment, price competition, and consumer recognition

Abstract

The concept “new retail” in e-commerce is to establish an offline channel and integrate it with the online retail channel. The development of new retail encounters three main problems: locations of the offline stores, the price competition with the traditional online retail, and the difficulty in consumer recognition in the two channels. In this paper, we present a duopoly model consisting of a new retail firm and an online firm, which sell the same product in two periods. The two firms compete for the market share using the behavior-based pricing (BBP), which means that in the second period each firm offers different prices to consumers with different purchasing histories/behaviors in the first period. We also solve the benchmark pricing model, where the histories/behaviors are not considered. The results of this paper provide valuable insights to the development of new retail in e-commerce. In the Nash equilibrium, each price of the new retail firm is higher than the corresponding price of the online firm due to a higher channel cost for the offline stores and high-speed deliveries. Under certain condition, the new retail firm will establish an offline channel with a larger hassle cost, which is a measure of the easiness of reaching the offline stores by the consumers, in the BBP model than that in the benchmark model. Interestingly, the difficulty in consumer recognition results in that the new retail firm occupies more market share and may obtain higher profit.

Appendix

Proof of Proposition 1

The o-firm’s profit is $\pi _o^\prime =(p_o^\prime -c_o)\frac{2(p_n^\prime -p_o^\prime )-v(1 -\alpha )}{2(h_o-h_n)}$. The optimal $p_o^\prime$ is given by the first order condition: $p_o^\prime =\frac{2c_o+2p_n^\prime -v(1-\alpha )}{4}$. The n-firm’s profit is $\pi _n^\prime =(p_n^\prime -c_n)(1-\frac{2(p_n^\prime -p_o^\prime ) -v(1-\alpha )}{2(h_o-h_n)})$. The optimal $p_n^\prime$ is given by the first order condition: $p_n^\prime =\frac{2c_n-2h_n+2h_o+2p_o^\prime +v(1-\alpha )}{4}$. Solve the two equations we obtain $p_o^\prime$ and $p_n^\prime$. The cutoff value $\theta ^\prime$ and the profits of the two firms are obtained by substituting $p_o^\prime$ and $p_n^\prime$. $\square$

Proof of Proposition 2

Substituting $c_n-c_o=A(h_o-h_n)^2$, conditions $2(c_n-c_o)-4(h_o-h_n)-v(1-\alpha )<0$ and $2(c_n-c_o)+2(h_o-h_n)-v(1-\alpha )>0$ determine that $\frac{\sqrt{4+2Av(1-\alpha )}-2}{2A}\le (h_o-h_n)\le \frac{2+\sqrt{4+2Av(1-\alpha )}}{2A}$.

Substituting $c_n-c_o=A(h_o-h_n)^2$ into the n-firm’s profit, we have:

$\pi _n^\prime =\frac{[-2A(h_o-h_n)^2+4(h_o-h_n)+v(1-\alpha )]^2}{36(h_o-h_n)}$. $\frac{\partial \pi _n^\prime }{\partial (h_o-h_n)}=\frac{[-(2(c_n-c_o)-4(h_o-h_n)-v(1-\alpha )]}{36(h_o-h_n)^2}[-6A(h_o-h_n)^2+4(h_o-h_n)-v(1-\alpha )]$, and $\frac{[-(2(c_n-c_o)-4(h_o-h_n)-v(1-\alpha )]}{36(h_o-h_n)^2}>0$. $-6A(h_o-h_n)^2+4(h_o-h_n)-v(1-\alpha )$ is positive and then negative as $h_o-h_n$ increases when $v(1-\alpha ) \le \frac{2}{3A}$. Thus, $\pi _n^\prime$ increases then decreases and $(h_o-h_n)^*$ is at $\frac{\partial \pi _n^\prime }{\partial (h_o-h_n)}=0$, that is, $(h_o-h_n)^*=\frac{2+\sqrt{4-6Av(1-\alpha )}}{6A}$.

When $v(1-\alpha )>\frac{2}{3A}$, $-6A(h_o-h_n)^2+4(h_o-h_n)-v(1-\alpha )$ is negative, so $\pi _n^\prime$ decreases as $(h_o-h_n)$ increases, $(h_o-h_n)^*=\frac{\sqrt{4+2Av(1-\alpha )}-2}{2A}$. $\square$

Proof of Lemma 1

The o-firm’s profit in the o-firm’s first-period market share is $\pi _{2o}^o=(p_o-c_o)\frac{p_{on}-p_{oo}}{h_o-h_n}$. The optimal $p_{oo}$ is given by the first order condition: $p_{oo}=\frac{c_o+p_{on}}{2}$. The n-firm’s profit is $\pi _{2o}^n=(p_{on}-c_n)(\theta _1-\frac{p_{on}-p_{oo}}{h_o-h_n})$. The optimal $p_{on}$ is given by the first order condition: $p_{on}=\frac{c_n-(h_n-h_o)\theta _1+p_{oo}}{2}$. Solving the two equations, we obtain $p_{oo}^*$ and $p_{on}^*$. $\square$

Proof of Lemma 2

The o-firm’s profit in the n-firm’s first-period market share is $\pi _{2n}^o=(p_{no}-c_o)(\frac{p_{nn}-p_{no}-v(1-\alpha )}{h_o-h_n}-\theta _1)$. The optimal $p_{no}$ is given by the first order condition: $p_{no}=\frac{c_o+p_{nn}-(h_o-h_n)\theta _1-v(1-\alpha )}{2}$. The n-firm’s profit is $\pi _{2n}^n=(p_{nn}-c_n)(1-\frac{p_{nn}-p_{no}-v(1-\alpha )}{h_o-h_n})$. The optimal $p_{nn}$ is given by the first order condition: $p_{nn}=\frac{c_n-(h_n-h_o)+p_{no}+v(1-\alpha )}{2}$. Solving the two equations, we obtain $p_{no}^*$ and $p_{nn}^*$. $\square$

Proof of Proposition 3

We substitute $\theta _1, p_{oo}^*, p_{on}^*, p_{no}^*, p_{nn}^*$ into the two firms’ profits. The two variables are $p_o$ and $p_n$. The profit functions are concave. The first order conditions give: $p_o=\frac{c_n+5c_o+3(h_o-h_n)+p_n-3v(1-\alpha )}{7}$ and $p_n=\frac{5c_n+c_o+5(h_o-h_n)+p_o-v(1-\alpha )}{7}$. Solving the two equations, we obtain $p_o$ and $p_n$. $\square$

Proof of Proposition 4

$c_n>c_o$ and $h_o>h_n$. So, $p_n-p_o=\frac{2(c_n-c_o)+(h_o-h_n)+v(1-\alpha )}{4}>0$. $v(1-\alpha )<(h_o-h_n)$, so $p_{on}-p_{oo}=\frac{18(c_n-c_o)+7(h_o-h_n)-v(1-\alpha )}{48}>0$, $p_{nn}-p_{no}=\frac{18(c_n-c_o)+23(h_o-h_n)+31v(1-\alpha )}{48}>0$, $p_{no}-p_{oo}=\frac{6(c_n-c_o)+5(h_o-h_n)+13v(1-\alpha )}{48}>0$, $p_{on}-p_{nn}=\frac{6(c_n-c_o)+11(h_o-h_n)+19v(1-\alpha )}{48}>0$. $\square$

Proof of Proposition 5

The differences between the market shares of the o-firm and the n-firm in the two periods are: $so_1-sn_1=\frac{2(c_n-c_o)-(h_o-h_n)-v(1-\alpha )}{8(h_o-h_n)}$, and $so_2-sn_2=\frac{5[2(c_n-c_o)-(h_o-h_n)-v(1-\alpha )]}{8(h_o-h_n)}$. The difference between the profits of the two firms is $\pi _o-\pi _n= \frac{13[2(c_n-c_o)-(h_o-h_n)-v(1-\alpha )]}{24}$. $\square$

Proof of Proposition 6

$\frac{\partial \pi _n}{\partial (h_o-h_n)}=[1620A^2 (h_o-h_n)^2-3576A (h_o-h_n)+1847]-540Av(1-\alpha )-\frac{263v^2(1-\alpha )^2}{(h_o-h_n)^2}$. $\frac{\partial ^4 \pi _n}{\partial (h_o-h_n)^4}>0$. $\frac{\partial ^3 \pi _n}{\partial (h_o-h_n)^3}$ changes from negative to positive as $(h_o-h_n)$ increases. $\frac{\partial ^2 \pi _n}{\partial (h_o-h_n)^2}$ first decreases from a positive value, then increases, however, we cannot judge the value is positive or negative. We use the compel method. $\frac{\partial \pi _n}{\partial (h_o-h_n)}$ is larger than $\frac{135A^2(h_o-h_n)^2-343A(h_o-h_n)+132}{192}$, and smaller than $\frac{1620A^2(h_o-h_n)^2-3576A(h_o-h_n)+1847}{2304}$. From the monotonicity of the two functions, $\frac{\partial \pi _n}{\partial (h_o-h_n)}$ increases then decreases. Thus, $(h_o-h_n)^*$ satisfies $\frac{\partial \pi _n}{\partial (h_o-h_n)}=0$. $\square$

Proof of Proposition 7

When $v(1-\alpha )\le \frac{2}{3A}$, we substitute $h_o-h_n=\frac{2+\sqrt{4-6Av(1-\alpha )}}{6A}$ into $\frac{\partial \pi _n}{\partial (h_o-h_n)}$.

If $\frac{\partial \pi _n}{\partial (h_o-h_n)}\le 0$, that is, $v(1-\alpha ) \le \frac{53(\sqrt{6817}-2619)}{4096A}$, $h^*=(h_o-h_n)^* \ge \frac{2+\sqrt{4-6Av(1-\alpha )}}{6A}$.

If $\frac{\partial \pi _n}{\partial (h_o-h_n)}> 0$, that is, $v(1-\alpha ) > \frac{53(\sqrt{6817}-2619)}{4096A}$, $h^*=(h_o-h_n)^* < \frac{2+\sqrt{4-6Av(1-\alpha )}}{6A}$. When $v(1-\alpha )> \frac{2}{3A}$, we substitute $h_o-h_n=\frac{\sqrt{4+2Av(1-\alpha )}-2}{2A}$ into $\frac{\partial \pi _n}{\partial (h_o-h_n)}$. $\frac{\partial \pi _n}{\partial (h_o-h_n)}\le 0$, $h^*=(h_o-h_n)^* < \frac{\sqrt{4+2Av(1-\alpha )}-2}{2A}$. $\square$

Proof of Proposition 8

$\varDelta \pi _n=\frac{[v(1-\alpha )-3(h_o-h_n)][6(c_n-c_o)-3(h_o-h_n) -11v(1-\alpha )]}{96(h_o-h_n)}-\frac{[11(h_o-h_n)-6(c_n-c_o) +19v(1-\alpha )]^2}{2304(h_o-h_n)}$$>0$, which can be transformed to the form in the proposition. $\square$