# American Institute of Mathematical Sciences

## Simulation analysis between enterprise and consumer group based on evolutionary game

 1 School of Business Administration, University of Science and Technology Liaoning, Anshan 114051, China 2 School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China

*Corresponding author: Hua Li

Received  April 2019 Revised  May 2019 Published  February 2020

In this paper, an evolutionary game model between enterprises and consumer groups is constructed under the background of restraining the online false information of production and management of Enterprises. It innovatively incorporates the parameter of consumer group's psychological recognition with enterprises into the construction of the model. Through the analysis of the stability of the model and the data simulation using Netlogo, it is found that the choice of enterprises and consumer groups under the Online False Information is related to the following parameters: Firstly, the additional cost and additional income earned by the company in actively responding to false information. Secondly, the labor cost of the consumer group to investigate false information and the opportunity cost of finding alternatives. Finally, the real information released by the enterprise and the psychological recognition of the consumer group to the enterprise. This study provides a theoretical basis and reference for the behavior and strategy selection of enterprises and consumer groups in the context of false information.

Citation: Qiubai Sun, Bowen Li, Hua Li, Xuebo Chen. Simulation analysis between enterprise and consumer group based on evolutionary game. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020266
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##### References:
Simulation of game strategy between enterprises and consumer groups
Simulation of game strategy between enterprises and consumer groups
Simulation of game strategy between enterprises and consumer groups
Simulation of game strategy between enterprises and consumer groups
Simulation of game strategy between enterprises and consumer group
Simulation of game strategy between enterprises and consumer groups
Simulation of game strategy between enterprises and consumer groups
Parameters and Symbol Explanations
 Parameters Symbol Explanations $C$ The cost of enterprises' negative response to false information $\Delta$C The additional cost of enterprises' active response to false information (such as investigation, evidence collection and refuting rumors, etc.) $I$ Income earned when enterprises negatively respond to false information $\Delta I$ Additional income earned when enterprises actively respond to false information $L$ When consumer groups choose not to buy, the loss suffered by enterprises caused by false information in addition to the cost (such as the decline in purchase volume and the trust level of consumer groups) $\lambda$ The psychological recognition of consumer groups on enterprises (the higher the trust, the lower the loss caused by the false information to enterprises, and the higher the utilization degree of the statement issued by enterprises by consumer groups when investigating the false information. The range is $0<\lambda<1)$ $H$ The efforts paid by consumer groups when investigating false information when enterprises negatively respond to false information $T$ The opportunity cost of consumer groups when abandoning the purchase of the product in order to find a new substitute $M$ Authentic information released by enterprises with active response $x$ Probability of enterprises choosing to respond actively $(\le x\le 1)$ $y$ Probability of consumer groups choosing to buy products $(\le y\le 1)$
 Parameters Symbol Explanations $C$ The cost of enterprises' negative response to false information $\Delta$C The additional cost of enterprises' active response to false information (such as investigation, evidence collection and refuting rumors, etc.) $I$ Income earned when enterprises negatively respond to false information $\Delta I$ Additional income earned when enterprises actively respond to false information $L$ When consumer groups choose not to buy, the loss suffered by enterprises caused by false information in addition to the cost (such as the decline in purchase volume and the trust level of consumer groups) $\lambda$ The psychological recognition of consumer groups on enterprises (the higher the trust, the lower the loss caused by the false information to enterprises, and the higher the utilization degree of the statement issued by enterprises by consumer groups when investigating the false information. The range is $0<\lambda<1)$ $H$ The efforts paid by consumer groups when investigating false information when enterprises negatively respond to false information $T$ The opportunity cost of consumer groups when abandoning the purchase of the product in order to find a new substitute $M$ Authentic information released by enterprises with active response $x$ Probability of enterprises choosing to respond actively $(\le x\le 1)$ $y$ Probability of consumer groups choosing to buy products $(\le y\le 1)$
The Income Matrix between Enterprises and Consumer Groups
 Consumer Groups Buying Not Buying Enterprises Active $(I+\Delta I-C-\Delta C-(1-\lambda )L, \lambda M-H)$ $(-C-\Delta C-L, -T)$ Response $(I-C-(1-\lambda )L, -H)$ $(-C-L, -T)$
 Consumer Groups Buying Not Buying Enterprises Active $(I+\Delta I-C-\Delta C-(1-\lambda )L, \lambda M-H)$ $(-C-\Delta C-L, -T)$ Response $(I-C-(1-\lambda )L, -H)$ $(-C-L, -T)$
Formulas of Determinant and Trace of Jacobian Matric for Each Equilibrium Point
 Equilibrium Point $detJ$ $trJ$ $G_{1}(0, 0)$ $\Delta C(H-T)$ $T-H-\Delta C$ $G_{2}(0, 1)$ $(\Delta I-\Delta C)(H-T)$ $\Delta I-\Delta C+H-T$ $G_{3}(1, 0)$ $\Delta C(\lambda M-H+T)$ $\Delta C+\lambda M+T-H$ $G_{4}(1, 1)$ $(\Delta I-\Delta C)(\lambda M-H+T)$ $(\Delta I-\Delta C)(T-H)$ $G_{5}((H-T)/\lambda M, \Delta C/\Delta I)$ $(H-T)\Delta C(\Delta I-\Delta C)(H-T-\lambda M)/\Delta I\lambda M$ 0
 Equilibrium Point $detJ$ $trJ$ $G_{1}(0, 0)$ $\Delta C(H-T)$ $T-H-\Delta C$ $G_{2}(0, 1)$ $(\Delta I-\Delta C)(H-T)$ $\Delta I-\Delta C+H-T$ $G_{3}(1, 0)$ $\Delta C(\lambda M-H+T)$ $\Delta C+\lambda M+T-H$ $G_{4}(1, 1)$ $(\Delta I-\Delta C)(\lambda M-H+T)$ $(\Delta I-\Delta C)(T-H)$ $G_{5}((H-T)/\lambda M, \Delta C/\Delta I)$ $(H-T)\Delta C(\Delta I-\Delta C)(H-T-\lambda M)/\Delta I\lambda M$ 0
The Evolutionary Stability Strategy Summary
 $G_{1}(0, 0)$ $G_{2}(0, 1)$ $G_{3}(1, 0)$ $G_{4}(1, 1)$ $G_{5}((H-T)/\lambda M, \Delta C/ \Delta I)$ detJ trJ Stability detJ trJ Stability detJ trJ Stability detJ trJ Stability detJ trJ Stability (1) + - ESS + + Unstable + + Unstable + - ESS - 0 Saddle Point (2) + - ESS + + Unstable - ? Saddle Point - - Saddle Point / / / (3) + - ESS - ? Saddle Point + + Unstable - + Saddle Point / / / (4) + - ESS - ? Saddle Point - ? Saddle Point + + Unstable / / / (5) - ? Saddle Point - ? Saddle Point + + Unstable + + Unstable / / / (6) - ? Saddle Point + - ESS + + Unstable - - Saddle Point / / /
 $G_{1}(0, 0)$ $G_{2}(0, 1)$ $G_{3}(1, 0)$ $G_{4}(1, 1)$ $G_{5}((H-T)/\lambda M, \Delta C/ \Delta I)$ detJ trJ Stability detJ trJ Stability detJ trJ Stability detJ trJ Stability detJ trJ Stability (1) + - ESS + + Unstable + + Unstable + - ESS - 0 Saddle Point (2) + - ESS + + Unstable - ? Saddle Point - - Saddle Point / / / (3) + - ESS - ? Saddle Point + + Unstable - + Saddle Point / / / (4) + - ESS - ? Saddle Point - ? Saddle Point + + Unstable / / / (5) - ? Saddle Point - ? Saddle Point + + Unstable + + Unstable / / / (6) - ? Saddle Point + - ESS + + Unstable - - Saddle Point / / /
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