Management Science and Engineering
Vol. 07  No. 04 ( 2018 ), Article ID: 27507 , 11 pages
10.12677/MSE.2018.74027

Modelling a New Relation between the Consumption Decision and Psychological Distance of Online Consumers

—Based on Maximum Entropy Principle

Jiaoli Suo, Dongmei Zhao

College of Economics and Management, China Agricultural University, Beijing

Received: Oct. 22nd, 2018; accepted: Nov. 6th, 2018; published: Nov. 13th, 2018

ABSTRACT

In the age of e-commence, numerous characteristics of psychic distance are distinct from that of traditional markets. To better understand these differences, in this present paper, we established a new relationship between consumption decision and psychological distance of online consumers by making use of the Maximum Entropy Principle. According to the classification of the commodities online, we focus on printed books and digital products. Data were collected from the China-based B2C e-commerce platform, Jingdong and Alibaba’s Taobao Mall, by convenience sampling. Data collection yielded 302 valid questionnaires. The results showed that the psychological distance has a negative influence on the consumption decision of online consumers; the three dimensions of psychological distance can significantly influence the online consumer buying behavior, and the impact from high to low in order is: time distance, social distance and spatial distance. By this technique, an in-depth methodology for establishing the interaction between the consumption decision and psychological distance is presented for better marketing strategy of e-business.

Keywords:Psychological Distance, Consumption Decision, Maximum Entropy Principle, Online Consumer, E-Commence

—基于最大熵原理

Copyright © 2018 by authors and Hans Publishers Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

1. 引言

2. 熵与最大熵原理

$S=k\mathrm{log}W,$ (2.1)

$H=-K\sum _{i}{P}_{i}\mathrm{ln}{P}_{i}\text{ }\text{ }.$ (2.2)

1) 离散型

$H=-\sum _{i=1}^{n}{p}_{i}\mathrm{ln}{p}_{i}.$ (2.3)

$\sum _{i=1}^{n}{p}_{i}=1,\text{\hspace{0.17em}}{p}_{i}\ge 0,i=1,2,\cdots ,n\text{\hspace{0.17em}}.$ (2.4)

$\begin{array}{l}\sum _{i=1}^{n}{p}_{i}=1,{p}_{i}\ge 0,i=1,2,\cdots ,n\text{\hspace{0.17em}};\\ \sum _{i=1}^{n}{p}_{i}{x}_{i}=E.\end{array}$ (2.5)

2) 连续型

$H=-\int f\left(x\right)\mathrm{ln}f\left(x\right)\text{d}\left(x\right).$ (2.6)

$H=\int f\left(x\right)\text{d}\left(x\right)=1,\text{\hspace{0.17em}}\left(f\left(x\right)\ge 0\right).$ (2.7)

$\begin{array}{l}\int f\left(x\right)\text{d}x=1\text{ };\\ \int xf\left(x\right)\text{d}x=E.\end{array}$ (2.8)

3. 心理距离与决策行为关系模型构建

$W=\left(\begin{array}{c}P\\ {p}_{0},{p}_{1},\cdots ,{p}_{n}\end{array}\right)=P!/\prod _{i=0}^{n}{p}_{i}!.$ (3.1)

$H=\mathrm{ln}W=\mathrm{ln}P!\text{\hspace{0.17em}}-\sum _{i=0}^{n}\mathrm{ln}{p}_{i}!.$ (3.2)

$\sum _{i=0}^{n}{p}_{i}=P;$ (3.3)

$\sum _{i}2\text{π}i{p}_{i}={P}_{0},$ (3.4)

$L\left({p}_{i}\right)=\mathrm{ln}P!\text{\hspace{0.17em}}-\sum _{i=0}^{n}\mathrm{ln}{p}_{i}!+{\lambda }_{1}\left(P-\sum _{i=0}^{n}{p}_{i}\right)+{\lambda }_{2}\left({P}_{0}-\sum _{i=0}^{n}2\text{π}i{p}_{i}\right).$ (3.5)

${p}_{i}={\text{e}}^{-{\lambda }_{1}}\cdot {\text{e}}^{-2\text{π}i{\lambda }_{2}}.$ (3.6)

${\int }_{0}^{R}2\text{π}r{\text{e}}^{-{\lambda }_{1}}\cdot {\text{e}}^{-2\text{π}r{\lambda }_{2}}\text{d}r={P}_{0}.$ (3.7)

$p\left(r\right)=2\text{π}{\lambda }_{2}^{2}{P}_{0}{\text{e}}^{-2\text{π}r{\lambda }_{2}}.$ (3.8)

${\rho }_{0}=2\text{π}{\lambda }_{2}^{2}{P}_{0}$ (3.9)

${\rho }_{0}=\frac{{P}_{0}}{2\text{π}{r}_{0}^{2}}.$ (3.10)

$p\left(r\right)={\rho }_{0}{\text{e}}^{-r/{r}_{0}}.$ (3.11)

$PD=\alpha TD+\beta {S}_{social}D+\gamma {S}_{spatial}D,$ (3.12)

$p\left(x,y,z\right)={\rho }_{0}{\text{e}}^{-\left(\alpha x+\beta \delta y+\gamma z\right)/{r}_{0}}.$ (3.13)

(3.14)

${p}^{\prime }\left(x,y,z\right)={{\rho }^{\prime }}_{0}{\text{e}}^{-\left({\alpha }^{\prime }x+{\beta }^{\prime }y+{\gamma }^{\prime }z\right)/{r}_{0}}.$ (3.15)

$\upsilon =\frac{{p}^{\prime }\left(x,y,z\right)}{p\left(x,y,z\right)}={{\rho }^{\prime }}_{0}/\rho \cdot {\text{e}}^{\left(\left(\alpha -{\alpha }^{\prime }\right)x+\left(\beta -{\beta }^{\prime }\right)y+\left(\gamma -{\gamma }^{\prime }\right)z\right)/{r}_{0}}$ (3.16)

4. 模型验证

Table 1. Measure of time distance

Table 2. Measure of social distance

Table 3. Measure of spatial distance

Table 4. Results of fitting curve in (3.18)

Figure 1. A decreasing surface meaning the relation between purchase rate and time distance and spatial distance

Figure 2. A decreasing surface meaning the relation between purchase rate and social distance and spatial distance

Figure 3. A decreasing surface meaning the relation between purchase rate and time distance and social distance

5. 结论

Modelling a New Relation between the Consumption Decision and Psychological Distance of Online Consumers[J]. 管理科学与工程, 2018, 07(04): 233-243. https://doi.org/10.12677/MSE.2018.74027

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